Thank goodness I don't live in America with gun shots going off all the time and no one blinking an eye!!!
My advise is if you are having predator problems... house your birds in a SECURE, WELL BUILT coop and run... = no problems ever!
If you want to waste your time trapping animals, loosing birds, killing animals, trapping animals, loosing birds, killing animals... over and over again for years.. then that's your call... maybe you have a lot of time on your hands and nothing better to do?
Myself, I don't want predators to kill my birds... nor do I want to shoot native wildlife that is just trying to survive. I get pleasure from my domestic animals.. and also seeing wildlife about... and I take the effort to keep my animals in predator proof enclosures which are well built and last for years.