Is Brutus still a fatalist in act 5 of Julius Caesar?

"The fault, dear Brutus, is not in our stars, / But in ourselves, that we are underlings," Cassius says to Brutus when he tries to convince him to join the conspiracy to assassinate Julius Caesar (1.2.141-42). Here we see Cassius reject fate, and Brutus ultimately agrees with him, taking responsibility for keeping Rome “free” by killing Caesar to prevent him from becoming a despot.  This is one reason we can understand Brutus as a tragic hero, for if he blamed everything on fate, he would have learn nothing.  At the end of the play he chooses to die nobly, on his own sword, because he knows he cannot win and has not brought the freedom to Rome that he thought he would by assassinating Caesar.  Antony calls him a great man at the end of the play for this very reason: he did what he thought was right, took responsibility for that, and died for that.  Had he attributed everything to fate, he would not have been a great man.