[tex]\sqrt{3}cosA+2cosB+2\sqrt{3}cosC=4<=>-\sqrt{3}cos(B+C)+2cosB+2\sqrt{3}cosC=4<=>-\sqrt{3}sinBsinC+\sqrt{3}cosBcosC+2cosB+2\sqrt{3}cosC=4<=>\left ( \sqrt{\frac{3}{2}}sinC-\frac{sinB}{\sqrt{2}} \right )^2+\left ( \sqrt{\frac{3}{2}}cosC+\frac{cosB}{\sqrt{2}} -\sqrt{2}\right )^2=0[/tex]