If your goal is to "trap them out" I agree that is extremely difficult, basically impossible. If there is one there will be more. Artichoke Lover's stated goal is reduce the risk. That was also my goal when I was in Arkansas and trapping and eliminating a dozen or more raccoons a year. Not exterminating them but reducing their damage.
When I trapped and eliminated the one that was eating my blackberries just as they were getting ripe I started getting ripe blackberries.
@catjac1975 the same thing happened when I one got the one that was getting into my corn. I stopped finding chewed up apples when I got that one. It took more effort when I tried to use an Adirondack mouse trap, I had to get some possum as well as raccoons to stop them getting the bait and bashing the trap. I did get to the point I could play with that mouse trap but I switched to other mouse traps because I knew another raccoon or possum would eventually show up. When I removed several skunks in the area my dogs were sprayed a lot less often. I think one dog having a learning curve may have helped her but the other one didn't seem to be able to learn that lesson.
Those were all after specific targets. I also believe that if you can thin out the ones hunting your land you can reduce the numbers that are hunting your land so you will lose less to them. That's not a long term or permanent solution, others will show up. If not immediately then when their Mommy weans them and they go off looking for their own territory to hunt. To me the only long term solution to raccoons or other such "predators" are suitable and well maintained barriers. You may be able to enclose a small chicken coop and run well enough to keep raccoons out but for something like most of our gardens and larger chicken runs that just about has to involve electricity.
I do not feel that my attempts to trap them and reduce the numbers that were hunting my land (and targeting certain ones) was a waste of time and energy, but I agree that trying to trap them out to totally and forever eliminate them is an unrealistic goal.