[จูกัดเหลียง]

Let $a,b,c>0$ and $a+b+c=3$
Prove that $$\frac{a}{a^2+1}+\frac{b}{b^2+1}+\frac{c}{c^2+1}\le \frac{1}{a^4+1}+\frac{1}{b^4+1}+\frac{1}{c^4+1}$$