If \(x - \frac{1}{x} = y, y-\frac{1}{y} = z, z-\frac{1}{z} = x\), there which of the following equations are true ?
A. \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\)
B. \(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=8\)
C. \(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}=-3\)
Choose the correct answer from the options given below: