If $\cos \theta = \frac{-1}{2}$ and $0^o < \theta < 360^o$,then the values of $\theta$ are

The value of $\cos y \cos (\frac{\pi}{2} - x) - \cos (\frac{\pi}{2} - y) \cos x + \sin y \cos (\frac{\pi}{2} - x) + \cos x \sin (\frac{\pi}{2} - y)$ is zero,if

The number of solutions of the equation $x + 2 \tan x = \frac{\pi}{2}$ in the interval $[0, 2\pi]$ is:

The number of values of $x$ for which $\sin 2x + \sin 4x = 2$ is

The sum of the solutions in $(0, 2\pi)$ for the equation $\cos x \cos \left(\frac{\pi}{3}-x\right) \cos \left(\frac{\pi}{3}+x\right) = \frac{1}{4}$ is

If $\cos(\alpha - \beta) = 1$ and $\cos(\alpha + \beta) = 1/e$,where $\alpha, \beta \in [-\pi, \pi]$,the number of pairs of $(\alpha, \beta)$ which satisfy both equations is: