ÖMO 2015 Problem 4

Let $x,y,z$ be positive real numbers with $x+y+z \ge 3$ . Prove that $\frac{1}{x+y+z^2} + \frac{1}{y+z+x^2} + \frac{1}{z+x+y^2} \le 1$ When does equality hold?

(Karl Czakler)