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1: You've uploaded the spec to the Templars. Saman congratulates you and tells you to destroy the Dentons and use machine in the statue. There are now three Illuminati Elite Guards here in the UNATCO HQ building. You can cloak past them all to the exit or take them out. On your way out of the Aquinas Control room, head toward the stairs and you'll find an Illuminati Elite Guard (IEG) in the room just before the stairway. Another one is at the top of these stairs. Finally, the last IEG is past the two bums (with Bum Leader), up the stairs and in the next room where you got the flag for the special ending. Continue on and exit back to the West Side.
2: Just outside and up the ramp, there is no resistance, unlike with ApostleCorp and Illuminati's ending. Exit the UNATCO building and peek around the corner to the north toward the statue to see all of ApostleCorp gathered around the entrance, including JC and Paul Denton, Grays and three Hunter Seeker bots. If you want some additional help, you can find Leo in his comm van out back and enlist him to help take out the Dentons. At this point, by far the easiest way I found to deal with them is to snipe from afar using the scope, with silencer mod (and optionally, increased damage mod) attached. Stand near the corner, and take them down one by one. If you've got Leo, he'll be up there in the heat of the action helping.
4: Concentrate on the humonoids first, and they'll all simply scramble around not knowing which direction you are. When they're down, approach the Hunter Seekers and use whatever method you wish to disable them. Mag Rail alt-fire works great, as well as the Spy Drone.
5: Approach the Statue Entrance door, open it and if you have them, use your Cloak/Thermal Mask combo to approach the Helios Uplink Machine in the middle and use it. Surprisingly, JC will now return to life as a mortal human, and attack you. Exit the building, get as far away as you can to avoid his attacks, and use your Rocket Launcher or Mag Rail. Sniper works as well if you can get far enough behind him. There are many ways to defeat him, but staying out of his range is easiest, and strafe his rocket attacks. When he's dead, head into the statue and use the Helios Uplink Machine to see the ending! Congratulations on beating Deus Ex: Invisible War!