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. $$(\frac{2}{z})\Theta(\frac{2}{z})={z}$$