Was Hamlet insane or just pretending to be insane and why?

well i read it and it says that he was going to pretend to be crazy then at around the middle-end, he does go crazy but we dont see if he was crazy or not. even teachers and readers of the book cant determine if we was "actually" acting all crazy. the reason is that he was to get the truth out from his uncle for killing his father and blaming Hamlet for the murder so that he can be with Queen without Hamlet bothering him.