If $cot\Theta =sin2\Theta (where\Theta \neq n\pi ,n\ is\ an\ integer)\Theta$=?

$\cot\theta =\sin 2\theta$

$\Rightarrow \dfrac{\cos\theta}{\sin\theta}=2\sin\theta \cos\theta$

$\Rightarrow \cos\theta =2\sin^2\theta \cos\theta$

$\Rightarrow \cos\theta -2\sin^2\theta \cos\theta =0$

$\Rightarrow \cos\theta(1-2\sin^2\theta)=0$

$\Rightarrow \cos\theta(\cos 2\theta)=0$

$\Rightarrow \cos\theta =0$ or $\cos 2\theta =0$

$\Rightarrow \theta =\dfrac{\pi}{2}$ or $2\theta =\dfrac{\pi}{2}$

$\Rightarrow \theta =\dfrac{\pi}{4}$

$\therefore \theta$ can be $45^o$ or $90^o$.