Head over to the nearby locked door (Level 2 difficulty). if you can get through here, things will be a lot easier as you can ambush the Brutes who are waiting on the other side. You need to deal with 3 of them to get out of this basement. You can get away with killing as few as one of them easily. It helps some to kill them all. Head on out of the basement now.
Once you are on the ground floor you will want to look to the left. You will see 2 Extremists looking for you. Wait for them to start heading away from where you are. Slip into the room and then blend with one of the crowds. Wait for them to pass you then slip into the room they were just looking into. Go over to the left and pick the lock of the door there (Level 2). Break through there and head for the door on the right. Deal with the Extremist guarding the exit and you are out and free.