[จูกัดเหลียง]

Let $a,b,c>0$ and $a+b+c=3$ Prove that $$\frac{1}{\Big((a-b)^2+3bc+3ca\Big)^2}+\frac{1}{\Big((b-c)^2+3ca+3ab\Big)^2}+\frac{1}{\Big((c-a)^2+3ab+3bc\Big)^2}\ge \frac{1}{12}$$