What does Act 2 reveal about the mental state of Hamlet?

At the beginning of Act 2, we find that Hamlet has been quite successful in putting on his "antic disposition."  He has frightened Ophelia and fooled Polonius into thinking he is mad because Ophelia had broken off her relationship with Hamlet at Polonius' request.  Claudius believes that something else is up with Hamlet--which is true-- and wants to explore Hamlet's state of mind further.  Gertrude probably is closest to the truth of what is bothering Hamlet --his father's death and her hasty marriage.  We know that he is certainly despondent about this series of events.  We also know that he is acting.  Through his mad act, Hamlet has been able to ascertain whom he can trust.  He knows Ophelia will confide in her father who will go immediately to the king.  He knows that he cannot trust his former friends Rosencrantz and Guildenstern.  Despite what many readers think, Hamlet has proceeded cautiously and wisely in his revenge on Claudius.  His actions seem contrived to hide his pain and his true intention of revenge as well as to determine just how alone he truly is in his mission to commit regicide and patricide--crimes no one should take lightly. Hardly the thought processes of a truly insane person. Yet, he is overwhelmingly sad.  Denmark is a prison for him; loved ones have betrayed him; he is impatient to do something.  At the end of Act 2, Hamlet delivers what is probably his most emotional soliloquy: "Oh, what a rogue and peasant slave am I."  In this soliloquy, Hamlet is clearly angry that he has been unable to act directly on his revenge.  Maybe deep down he is also angry that he doesn't quite have the stomach for killing.  He compares himself to the actor who can become emotional over a fictional character, Hecuba, who means nothing to him.  Hamlet wonders what the actor would do if he had the "motive and cue for passion that I have."  So, Hamlet concocts another scheme: the play scene.  This scheme will confirm Claudius' guilt, and Claudius' reaction will motivate Hamlet to respond in kind.  What we see in Act 2 is the workings of a truly brilliant mind: one who is cautious, impatient, alienated, angry, and disillusioned--not one who is insane.