[จูกัดเหลียง]

Let $a,b,c>0$ with $abc=1$

Prove that $$\displaystyle 2\Big(\Big(\frac{a}{1+a+ab}\Big)^2+\Big(\frac{b}{1+b+bc}\Big)^2+\Big(\frac{c}{1+c+ca}\Big)^2\Big)+\frac{9}{(1+a+ab)(1+b+bc)(1+c+ ca)}\ge 1$$