TR-MO 2007 Problem 3

If $a,b,c$ are three positive real numbers such that $a+b+c=3$ , prove that ${\frac{a^{2}+3b^{2}}{ab^{2}(4-ab)}}+{\frac{b^{2}+3c^{2}}{bc^{2}(4-ab)}}+{\frac{c^{2}+3a^{2}}{ca^{2}(4-ca)}}\geq 4$