inequality between 3 square roots

Question

I'm breaking my head over this. If (a,b,c) are positive real, show that \begin{align} \sqrt{\frac{2a}{a+b}}+\sqrt{\frac{2b}{b+c}}+\sqrt{\frac{2c}{c+a}}\le3 \end{align}

(There is equality only when $a=b=c$)