Let $a, b, c$ be positive real numbers such that $a^2 + b^2 +c^2 +(a+b+c)^2 \le 4$. Prove that $$\frac{ab+1}{(a+b)^2}+\frac{bc+1}{(b+c)^2}+\frac{ca+1}{(c+a)^2}\ge 3$$