The operation \Theta is defined by {x}\Theta{y}=\frac{1}{x}+\frac{1}{y} for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true?
I. z\Theta(-z) = 0
II.{z}\Theta{\frac{z}{z-1}}={1}
III. (\frac{2}{z})\Theta(\frac{2}{z})={z}