The number of elements in the set $S=$ $\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\right.$ $\left.10 \cos ^{2} \theta+5=0\right\}$ is

If $\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0$, then $\theta = $

If $n$ is any integer, then the general solution of the equation $\cos x - \sin x = \frac{1}{{\sqrt 2 }}$ is

The equation $3\cos x + 4\sin x = 6$ has

Find the general solution of the equation $\cos 4 x=\cos 2 x$

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$.

Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to