No, that's the example I came up with in my head too. "Entrapment" is what happens when law enforcement coerces someone to commit a crime who was not otherwise inclined to do it. The kernel of entrapment isn't that law enforcement creates an opportunity to commit a crime, but that they accompany the opportunity with some kind of push or shove.

It's both. It'd be just blackmail if I did it to you. If I were a cop, it's additionally entrapment.