IR-TST 2009 Problem 3

Suppose that $a$ , $b$ , $c$ be three positive real numbers such that $a+b+c=3$ . Prove that :

$\frac{1}{2+a^{2}+b^{2}}+\frac{1}{2+b^{2}+c^{2}}+\frac{1}{2+c^{2}+a^{2}} \leq \frac{3}{4}$