In Australia to trap a whole herd of feral goats they put a fence around a water point, with the only entrance being a ramp which the goats walk up and jumps off. The problem for them is that they can’t jump back out! They can then be shot and processed.
Another modern way here is they will release a goat with a radio collar, this goat will find itself a herd and the shooters can track them down, they shoot all the goats, release another goat with a collar and repeat. It’s called the Judas method!