If $\sin \left(\frac{\pi}{4} \cot \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$, then the general solution of $\theta$ is

If $3 \sin 2 \theta=2 \sin 3 \theta$ and $0<\theta<\pi$, then the value of $\sin \theta$ is equal to

The possible values of $\theta \in(0, \pi)$ such that $\sin \theta+\sin (4 \theta)+\sin (7 \theta)=0$ are

If $\tan 3 \theta=\cot \theta$, then $\theta=$