The numbers of solution $(s)$ of the equation $\left( {1 - \frac{1}{{2\,\sin x}}} \right){\cos ^2}\,2x\, = \,2\,\sin x\, - \,3\, + \,\frac{1}{{\sin x}}$ in $[0,4\pi ]$ is

The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3sin^2x\, \,-\,\, 7sinx + 2 = 0$ is

The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to

The number of solutions of the equation $1 + {\sin ^4}\,x = {\cos ^2}\,3x,x\,\in \,\left[ { - \frac{{5\pi }}{2},\frac{{5\pi }}{2}} \right]$ is

The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is

Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$  If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal