Question 73
Find all possible values of a real number $a$ such that there exist pairwise distinct nonzero real numbers $x, y, z$ satisfying the equalities
$$
x - \frac{y}{z} - \frac{z}{y} = y - \frac{z}{x} - \frac{x}{z} = z - \frac{x}{y} - \frac{y}{x} = a.
$$
$$
x - \frac{y}{z} - \frac{z}{y} = y - \frac{z}{x} - \frac{x}{z} = z - \frac{x}{y} - \frac{y}{x} = a.
$$