Find all ordered triples $(x, y, z)$ of real numbers satisfying the following system of equations:

$$
\begin{aligned}
x^{3} & =\frac{z}{y}-2 \frac{y}{z} \\
y^{3} & =\frac{x}{z}-2 \frac{z}{x} \\
z^{3} & =\frac{y}{x}-2 \frac{x}{y}
\end{aligned}
$$