BALKAN-SL 2013 A1

Positive real numbers $a, b,c$ satisfy $ab + bc+ ca = 3$ . Prove the inequality $$\frac{1}{4+(a+b)^2}+\frac{1}{4+(b+c)^2}+\frac{1}{4+(c+a)^2}\le \frac{3}{8}$$