I also am battling a beaver...unsuccessfully I might add. But in the process I have got 3 nutria rats removed which hind sight I should have left them as they eat the aquatic vegetation(another issue on my property). I have found there den but I do not know how to trap or go about trapping them. I saw it once but did not have gun in hand and when I retrieved the one from my pickup it was gone. Hope you have better luck, wish I could give you some better advice. They do eat a lot of my tree's they seem to like to drop them more than eat them completely.