You hide from him. You hide with him. You move through the trees and the darkness with him, and stalk the same prey he stalks, until you can practically smell him in the air.
It will only be a matter of time before he finds you, waiting for him in one his hiding places. He'll step on you without even knowing that you're there -- and when the police respond to the report of a single shot fired they will only find another victim.
But this victim will have an AR-15 lying on the ground next to him. And when days and weeks pass without any more sniper attacks, the nation will speak in awe of the silent protector who vanished like a whisper.
Umm, This is a big place. You could be sitting in the dark for a long time smellng gas fumes.
But such methods has serious holes in the Asphalt Jungle involved here. I think if deployed in the numbers required to cover the DC/VA/MD area they'd be shooting each other and getting the right one would be analogious of winning the lotto.
Good points though, Stay Safe !!