In regards to Fahrenheit 451, which Shakespeare play does Beatty quote immediately before his death?
The quick answer to this is that he quotes from Julius Caesar.
Just before Montag kills him, Beatty is taunting Montag. It is pretty clear that he wants Montag to kill him. He tells Montag that he is some sort of a fake, a "second rate literatteur."
While taunting him, he quotes from something that Brutus says to Cassius in Julius Caesar. The lines he quotes come from Act IV, Scene 3 of that play.
By being able to quote so easily from Shakespeare, Beatty is making clear to us that he really is very well read. That is probably why he wants to die -- he secretly loves books and knowledge but is in a position where he has to try to destroy those things as his job.