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1: When Ava (or Sid) drops you off, talk to Crazy Wendy to learn of a secret tunnel entrance. Head north and deal with the Templar roaming nearby, and then again north up a small alleyway to a small boy named Billy next to a dumpster. Talk to him and pay him the 200 to get the "annotated" map shown above.
2: Mantle up the railing above the dumpster, hang a left and take out the flamethrower ground turret just around the corner with an EMP blast. Continue to a couple of stacked boxes leading to an upper ledge, where at the top are two Templars waiting for action. Make some noise to bring them close to the edge and take them down... or Cloak, mantle up and take them out once on top. Open the chest for TWO BLACK MARKET BIOMOD CANISTERS. By now, if you've upgraded like me, you'll have a stash of Black Market Canisters unused.
3: Another Templar is below the ledge to your left, near a stairway on the far end. Take him down from afar and this area will be clear. Jump down and open the grate near the dumpster. Climb down the ladder and Cloak halfway down. There's a security bot and another Templar further down here in the non-filled sewer. Take them out as you please (Spy Drone or Mag Rail alt-fire for security bot) and continue down until you reach the opening on your right with a red laser barrier. Beyond are another two Templars you can take down from behind the beams if you wait for them to appear.
4: Use your multitool or EMP blast on the beams and slip in the new corridor. You'll find a host of multitools on the tables as you make your way down. When you get to the end, take a right, face another Templar and enter an area with lockers and bunks. The left locker holds a Refire Rate Weapon Mod. On the other side of the lockers is a small corridor leading to a lift. Take it to the Templar Church.
5: At the top of the lift you'll encounter a camera on the far wall. Send your Spy Drone in or use your Mag Rails Alt-Fire and beware the three Templars in the adjoining room to the right. If they don't hear you, approach the next room and be prepared to deal with them. When they're taken care of, there's a ground turret in the middle of the room you'll want to disable as well. Next, you'll receive a message from Chad about hacking Saman's computer. Go to the back desk with holocomm and speak with Saman, and then read the datacube next to the holocomm for his login; how convenient.
6: Unlock the North Door (getting the key from the eastern stairwell and coming back isn't worth it IMO for a multitool), enter and view the holocomm a few times for different messages. Now use his login on the security terminal in the room to download the sequencing module as per Chad's directions, and exit the room. Make your way toward the yellow lasers at the front of the church, and enter the door to the right, before you reach them. Search both under the stairs and at the top for a couple of weapon mods and the softkey to Saman's chambers, which you've already entered, sitting on top of a crate. On your way back down, peek out the broken window and take care of a Templar Paladin on the outside from afar for convenience.
7: Drop down through the broken window, approach the area with the downed Paladin and you'll see an alcove with electric sparks. Use a multitool on the control box if you need to refill at the repairbot within. Head back to the southeast corner door outside, taking out the security bot on the way, and exit back to the Templar Compound. Make your way back to the drop off point and meet with Klara Sparks, whom you clue in about what's happening. Take the chopper back to Trier.
8: At the square, Lin-May Chen approaches you and you can either tell her about the Illuminati or lie, it makes no difference. You'll find out about her heritage and then get a series of coms directing you back to the lab to repair the Black Gate. Head back to Tracer Tong at the Nine Worlds and hear what he has to say about the Dentons and about reviving Paul. Exit and make your way back to the Black Gate Ruins. This time the SSC are fighting the Templars out in the courtyard. Join in if you wish, and then head upstairs to the secret entrance, taking the elevator to the Black Gate Laboratory.
9: This part is fairly simple. After the elevator ride, take a right and keep right until you pass up T. Tong's office. You'll come to a stairway and a ladder ahead. Take the maintenance ladder up and then use the vent on the left wall. Defeat a spider bot on your way down the long shaft, and emerge at the other end. On the right side between two gas barrels you'll find another softkey with the Security Beams code, and make sure to avoid the radiation barrels to your left (as you enter). Near the radioactive barrels on the wall is a control box. Use it to activate the Black Gate generator and turn off the sparks in the other room.
10: Exit out through the other end of this room and you'll see a door on your left, leading to a repairbot. Charge up, proceed past the darkened room with previously erratic generator and take the ladder back down. This time, use the stairs and unlock the door using the keycode you got back in T. Tong's office your last visit here. There's another Templar in the room, so after he's taken out, use your login to access the security terminal near the window. Once you begin the gate sequencing, watch as the teleporter comes to life. Head back downstairs, past Tracer Tong's office, take the first right, bypass the lasers and enter the Black Gate Reactor teleporter to Antarctica.