I feel I should point out that "Brute", being Latin vocative, should be pronounced "Broot-ay". I have painful memories of our school rehearsal of this scene, in which Caesar would repeatedly ask
Et tu, brute?
At which point the Head of Drama would once again put his head in his hands and weep.
Gritchka suggests this interesting interpretation of the switch to Latin: "Shakespeare, knowing his Suetonius, switched into Latin (which his audience would understand) to convey the real shift into Greek." That is, to capture the change in language in Caesar's original words, Shakespeare did the same: and just as Caesar's audience would have understood the Greek "Και συ, τεκνον;", so Shakespeare's understood Latin. A smart interpretation indeed.