Answer
$\frac{3}{4}$ , 0
Work Step by Step
Given expression is-
$\sin^{2}\theta$ , $\sin\theta^{2}$
Also given $\theta$ = $\frac{\pi}{3}$
$\sin^{2}\theta$ = $(\sin\theta )^{2}$ = $(\sin\frac{\pi}{3} )^{2}$ = $(\frac{\sqrt 3}{2})^{2}$ = $\frac{3}{4}$
$\sin(\theta)^{2}$ = $\sin(\frac{\pi}{3})^{2}$ = $\sin \frac{\pi^{2}}{9}$
= $\sin \frac{180\times180}{9}$ (Substituting $\pi = 180^{0}$)
= $\sin 3600^{0}$
Reference angle of 3600 will be 0
Therefore $\sin 3600^{0}$ = $\sin 0^{0}$ = 0
i.e. $\sin(\frac{\pi}{3})^{2}$ = 0
Hence
$(\sin\frac{\pi}{3} )^{2}$ = $\frac{3}{4}$
and $\sin(\frac{\pi}{3})^{2}$ = 0