\begin{matrix} sin^{2}x-(\sqrt{3}+1)sinxcosx+\sqrt{3}cos^{2}x=0 & \\ \Leftrightarrow \frac{sin^{2}x}{cos^{2}x}-(\sqrt{3}+1)\frac{sinx}{cosx}+\sqrt{3}=0 & \end{matrix}\begin{matrix}\Leftrightarrow tan^{2}x-(\sqrt{3}+1)tanx+\sqrt{3}=0 & \\\Leftrightarrow (tanx-1)(tanx-\sqrt{3})=0 & \end{matrix}