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

The solution of the equation $4{\cos ^2}x + 6$${\sin ^2}x = 5$

The value of $\theta $ in between ${0^o}$ and ${360^o}$ and satisfying the equation $\tan \theta + \frac{1}{{\sqrt 3 }} = 0$ is equal to

The number of solutions that the equation $sin5\theta cos3\theta  = sin9\theta cos7\theta $ has in $\left[ {0,\frac{\pi }{4}} \right]$ is

If $\sin \theta + \cos \theta = 1$ then the general value of $\theta $ is

If $m$ and $n$ respectively are the numbers of positive and negative value of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{9 \theta}{2}$, then $mn$ is equal to $.............$.