If ${\sec ^2}\theta = \frac{4}{3}$, then the general value of $\theta  $ is

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

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

The number of solutions of $sin \,3x\, = cos\, 2x$ , in the interval $\left( {\frac{\pi }{2},\pi } \right)$ is

The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is

The angles $\alpha, \beta, \gamma$ of a triangle satisfy the equations $2 \sin \alpha+3 \cos \beta=3 \sqrt{2}$ and $3 \sin \beta+2 \cos \alpha=1$. Then, angle $\gamma$ equals