Trigonometrical Equations question bank (Maths)

If $\cos(\alpha - \beta) = 1$ and $\cos(\alpha + \beta) = \frac{1}{e}$,where $-\pi \lt \alpha, \beta \lt \pi$,then the total number of ordered pairs $(\alpha, \beta)$ is:

If $\tan m\theta = \tan n\theta$,then the general values of $\theta$ are in