What is the climax of the play? How does this build up?

My teaching definition of the climax is "that point in the play where the end becomes the end." In other words, that point where the ending of the tragedy is inevitable. In a Shakespearean play, the climax must always happen in Act III. Therefore, the climax is the killing of Mercutio and then Romeo killing Tybalt. The families now have no way to reconcile.