Integrate:$\int \limits_0^{\large\frac{\pi}{2}} \sin x \sin 2x \;dx$

Question

$$\begin {array} {1 1} (a)\;\frac{4}{3} \\ (b)\;\frac{1}{3} \\ (c)\;\frac{3}{4} \\ (d)\;\frac{2}{3} \end {array}$$