Školjka

%V0 Prove that $$\frac{a}{b+2c+3d} +\frac{b}{c+2d+3a} +\frac{c}{d+2a+3b}+ \frac{d}{a+2b+3c} \geq \frac{2}{3}$$ for all positive real numbers $a,b,c,d$.