Romeo yells in defiance of the stars when he learns of Juliet's death. How does this directly contradict his feelings toward fate at the beginning of the play?

Romeo first mentions fate in act one, scene two, in reply to a servant of the Capulet household asking him if he can read. Romeo replies with, "Ay, mine own fortune in my misery." At this point in the story Romeo is in love (or at least he thinks he is) with Rosaline, but Rosaline doesn't requite his feelings. So in this quotation Romeo says that he is sick with love and thus miserable, and that he thinks his fortune, or fate, might be to be permanently miserable.
In act one, scene four Romeo mentions fate again, but this time in a much more ominous way. Before the party Romeo says to Mercutio that his "mind misgives / Some consequence yet hanging in the stars" which will "bitterly begin his fearful date" on that very night. In other words, Romeo has a sense that some terrible fate, or consequence, awaits him, that it starts to make its way to meet him from tonight, and that it will end in "untimely death." This is quite a horrible fate that Romeo senses for himself, but he then declares, almost dismissively, "He, that hath the steerage of my course, / Direct my sail." "He," in this quotation, is the personification of fate, and Romeo seems rather nonchalantly to accept that his fate, however terrible it might be, is not his own to control. He seems to accept, with no protest, that his fate is not his responsibility, or not something that he can do anything about. And with that, he heads to the party, exclaiming, "On, lusty gentlemen."
At the end of the play, Romeo declares that with his suicide he shall "shake the yoke of inauspicious stars." In other words, he will prevent fate from having any more say over his life by taking that life away from fate. This would seem to represent a stark contrast to his attitude earlier in the play. Earlier in the play he seems to accept, uncomplainingly, that his fate is not his own to control, but here, towards the end of the play, he insists, defiantly, on taking some control back.
However, it is also possible to infer that Romeo's attitude towards fate really hasn't changed that much at all, if we consider another quotation further on in his final soliloquy. Almost the very last words he utters before drinking the poison can be interpreted as a final address to (a personification of) fate: "come, unsavoury guide! Thou desperate pilot, now at once run on / The dashing rocks thy sea-sick weary bark!" The "guide," or "pilot" here arguably represents fate, and the "weary bark," or ship, represents Romeo's life. He is asking fate, therefore, to crash his (Romeo's) life against the "dashing rocks", and in doing so, destroy, or end it. If we follow this interpretation then Romeo's attitude towards fate really hasn't changed very much. He still, in the end, accepts that his life is not his own to control, and that fate shall ultimately decide what to do with it. Hence, in this quotation, he asks, or tells fate to end his life for him.

At the end of the play, Romeo's attitude to fate is stated as "I defy you, stars!" when he hears of Juliet's death. He continues in this vein when he determines that he will kill himself, shaking "the yoke of inauspicious stars" from his person; that is, he thinks that by killing himself, he will be avoiding whatever fate has planned for him, when actually it is this act which leads to the final tragedy, as it causes Juliet to kill herself also.
At the beginning of the play, Romeo is concerned about what fate has in store for him (act 1, scene 3). He says his "mind misgives / Some consequence yet hanging in the stars" which will lead to his own untimely death. So, he thinks fate has an untimely death stored for him; and yet later he declares that he is defying fate by causing his own untimely death. One interpretation is that Romeo feels, in choosing the time and manner of his own death, he is at least preventing fate from determining that, too.