$\frac{\operatorname{Sin}3x}{\operatorname{Sin}x}=2{{\operatorname{Cos}}^{2}}x\xrightarrow{\times \operatorname{Sin}x\ne 0}\operatorname{Sin}3x=2\operatorname{Sin}x{{\operatorname{Cos}}^{2}}x$ $\Rightarrow \operatorname{Sin}(2x+x)=(2\operatorname{Sin}x\operatorname{Cos}x)\operatorname{Cos}x$ $\Rightarrow \operatorname{Sin}2x\operatorname{Cos}x+\operatorname{Cos}2x\operatorname{Sin}x=\operatorname{Sin}2x\operatorname{Cos}x$ $\Rightarrow \operatorname{Cos}2x\operatorname{Sin}x=0\xrightarrow{\operatorname{Sin}x\ne 0}\operatorname{Cos}2x\to 2x=k\pi +\frac{\pi }{2}\Rightarrow x=\frac{k\pi }{2}+\frac{\pi }{4}$