Number of solution$(s)$ of the equation $\sin 2\theta  + \cos 2\theta  =  - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ is-

Find the general solution of the equation $\cos 3 x+\cos x-\cos 2 x=0$

Solve $\sin 2 x-\sin 4 x+\sin 6 x=0$

The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta  = 2,$ is

If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi  =$ ....$^o$

Let,$S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^{2} \theta}+8^{2 \cos ^{2} \theta}=16\right\}$. Then $n ( S )+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is equal to.