Solve $\cos x = \frac{1}{2}$

The general solutions of the equation $\tan^2 \theta + \sec 2\theta = 1$ are

If $\cos 2x = (\sqrt{2}+1)(\cos x - \frac{1}{\sqrt{2}})$ and $\cos x \neq \frac{1}{\sqrt{2}}$,then $x \in$

The solution of $\frac{1}{2} + \cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is:

If $\sin 3 \theta = \sin \theta$,how many solutions exist such that $-2 \pi < \theta < 2 \pi$?

If $m$ and $n$ respectively are the numbers of positive and negative values 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 $.............$.