$\frac{3\operatorname{sinx}-4{{\sin }^{3}}x}{\operatorname{sinx}}=2{{\cos }^{2}}x\Rightarrow \frac{\operatorname{sinx}\left( 3-4{{\sin }^{2}}x \right)}{\operatorname{sinx}}=2{{\cos }^{2}}x$   $\xrightarrow{\operatorname{sinx}\ne 0}3-4{{\sin }^{2}}x=2{{\cos }^{2}}x\Rightarrow 3-4{{\sin }^{2}}x=2(1-{{\sin }^{2}}x)$  $\Rightarrow 3-4{{\sin }^{2}}x=2-2{{\sin }^{2}}x\Rightarrow 2{{\sin }^{2}}x=1\Rightarrow {{\sin }^{2}}x=\frac{1}{2}\Rightarrow \operatorname{sinx}=\pm \frac{\sqrt{2}}{2}\Rightarrow x=\frac{k\pi }{2}+\frac{\pi }{4}$