Zoroaster, Zarathustra, and Nietzsche, what is the relationship here?

Well, I'm more or less familiar with Nietzsche and his works like Beyond Good and Evil, On a Geneology of Morals, and the profound Thus Spoke Zarathustra. All of that work contains philosophy that is far out enough, but then last night as I was watching a History Channel presentation called The History of God, the narrator brought up the ancient religion of Zoroastrianism. Still far out but nothing that sparked my interest there until the narrator brought up the subject of Zarathustra and how Zarathustra was supposed to be an actual person and a prophet of some kind for the Zoroastrians. Thus I thought, hey Zarathustra is a pretty rare name for anybody so what are the chances that Zoroastrianism and Nietzsche both speak of this almost mythological personage known as Zarathustra? Is there a history to this? Any kind of relationship between Nietzsche, Zarathustra, and Zoroaster? Or is all that I completely huge coincidence? Cue the 2001: A Space Odyssey (Thus Spoke Zarathustra) track with the trumpets blasting now!