If the equation $\sin 3\theta - \cos^2\theta = \dfrac{1}{4}$ and $\theta \in [0, \pi]$, then the number of solutions is...

The general solution of the equation $\cot\theta \cdot \cot 2\theta = 1$ is...

If $0 \leq x \leq \dfrac{\pi}{2}$ , then the number of values of $x$ for which $\sin x - \sin 2x + \sin 3x = 0$ is

If $\sec 4\theta - \sec 2\theta = 2$, then $\theta =$