If $\sqrt{3} \tan \theta=3 \sin \theta$, find the value of $\sin \theta$.
Given : $\sqrt{3} \tan \theta=3 \sin \theta$
$\sqrt{3} \tan \theta=3 \sin \theta$
$\Rightarrow \sqrt{3} \frac{\sin \theta}{\cos \theta}=3 \sin \theta$
$\Rightarrow \frac{\sqrt{3} \sin \theta}{\cos \theta}-3 \sin \theta=0$
$\Rightarrow \frac{\sqrt{3} \sin \theta-3 \sin \theta \cos \theta}{\cos \theta}=0$
$\Rightarrow \sqrt{3} \sin \theta-3 \sin \theta \cos \theta=0$
$\Rightarrow \sqrt{3} \sin \theta(1-\sqrt{3} \cos \theta)=0$
$\Rightarrow \sin \theta=0$ or $1-\sqrt{3} \cos \theta=0$
$\Rightarrow \sin \theta=0$ or $\cos \theta=\frac{1}{\sqrt{3}}$
$\Rightarrow \sin \theta=0$ or $\cos ^{2} \theta=\frac{1}{3}$
$\Rightarrow \sin \theta=0$ or $1-\cos ^{2} \theta=1-\frac{1}{3}$
$\Rightarrow \sin \theta=0$ or $\sin ^{2} \theta=\frac{2}{3}$
$\Rightarrow \sin \theta=0$ or $\sin \theta=\sqrt{\frac{2}{3}}$
Hence, the value of $\sin \theta$ is 0 or $\sqrt{\frac{2}{3}}$.
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