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 $\theta=$

The general solution of the equation $\sqrt{3} \cos \theta+\sin \theta=\sqrt{2}$ is

Let $P=\{\theta / \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $Q=\{\theta / \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets, then