“Clear out the Taken infestation int he tunnels underneath the Cosmodrome.”
Make your way down deeper into the building. Head over to the right when you make it to the basement level. Clear out the Taken in this room just to make things easier. After that, head into the hole in the wall and start down toward the sewers.
With most of the Taken defeated, head down the stairs. This leads down to the water way of the sewer. Clear out the Taken and then move over to the right. Follow the water way forward and through the hole in the wall. Clear those Taken out of there and turn to the left.
Go through the doorway in front of you. Head straight into the room. You have to head to the back, where the marker is. This will trigger a Taken Captain. Clear them and the other Taken. Defeat them to trigger the next part of the mission.