Enter the room and defeat the Drones attacking you. Proceed to the balcony. Grab the Hammer of Dawn, it's near the door to the balcony. Go outside and use the Hammer to exterminate another Seeder and some more Drones. An ammo box can be found here. Move back into the room and listen to the dialog. The enemies will come through a sealed door to the left. Fight them off, then enter the corridor and turn right. Continue moving and reach another turn, proceed further and you'll find some ammo and a revolver. It's a great and very powerful sidearm, but has only six bullets when fully loaded, so count your shots.
Proceed to the next room and fight off the bad guys here, then continue following your team. Before the turn to left, there's a small room to your right with some ammo in it. Next room will have a Troika gunner at the far end, so run in quickly and dive into a doorway to your right. Fight your way through several linked rooms, and you'll find yourself behind the gunner; I believe you know what to do... Quickly grab the Troika then and lay down fire on the Wretches running through the corridor.
Follow your team, and you will come out in another corridor. Go down to the right if you need some ammo, then turn around and move the other way. Continue running until you reach a room with an ammo box and a shotgun as well as some Drones shooting from the room across. Deal with them, then pick up all the ammunition and grenades and proceed further. Afther a couple of turns, you will find your teammates near the stairs. Go up and listen to the dialogue (or rather, a trilogue) and climb up the next stairway, where another unsuspecting Troika gunner is shooting down at the Alpha team. Shoot him and take the Troika - there are many Drones down the street, so rain fire upon them for good. Sometimes an enemy will take cover and don't come out for a long time, so it can take a while to root him out. You'll be noticed when the fight is over and a cinematic will start.