Question 73
Let $x$, $y$, $z$ be real numbers satisfying the equation $x+y+z = x y + y z + z x$. Prove the inequality
$$
\frac{x}{x^{2}+1} + \frac{y}{y^{2}+1} + \frac{z}{z^{2}+1} \geq -\frac{1}{2}
$$
$$
\frac{x}{x^{2}+1} + \frac{y}{y^{2}+1} + \frac{z}{z^{2}+1} \geq -\frac{1}{2}
$$