The equation of the tangent to the curve $\mathrm{y} = 2\sin \mathrm{x} + \sin 2\mathrm{x}$at $\mathrm{x} = \frac{\mathrm{\pi }}{3}$ is

$$\begin{gathered} \mathrm{y} = 2\sin \mathrm{x} + \sin 2\mathrm{x} \mathrm{at} \mathrm{x} = \frac{\mathrm{\pi }}{3}, \mathrm{y} = \frac{3\sqrt{3}}{2} \\ \mathrm{m} = \frac{\mathrm{dy}}{\mathrm{dx}} = 2\cos \mathrm{x} + 2\cos 2\mathrm{x} \\ \mathrm{slope} \mathrm{of} \mathrm{tangent}= \cancel{2}\frac{1}{\cancel{2}} + \cancel{2} \times \left(\frac{-1}{\cancel{2}}\right) = 0 \end{gathered}$$Equation of Tangent is $$\begin{gathered} \mathrm{Equation} \mathrm{of} \mathrm{tangent} \mathrm{is} \left(\mathrm{y} - \frac{3\sqrt{3}}{2}\right) = 0\left(\mathrm{x} -\frac{\mathrm{\pi }}{3}\right) \\ \Rightarrow 2\mathrm{y} = 3\sqrt{3} \end{gathered}$$