Find value of k if sin^-1[ k tan (2 cos^-1 (√ 3)/2)]=(π)/3

$$\mathrm{k} \tan \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)=\sin \frac{\pi}{3} $$ $\displaystyle \Rightarrow \mathrm{ktan}\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}$ $\displaystyle \Rightarrow \mathrm{k} \sqrt{3}=\frac{\sqrt{3}}{2} \quad \therefore \mathrm{k}=\frac{1}{2}$