The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is

The solution of equation ${\cos ^2}\theta + \sin \theta + 1 = 0$ lies in the interval

The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is

If $\cos p\theta = \cos q\theta ,p \ne q$, then

The general value of $\theta $satisfying the equation $2{\sin ^2}\theta - 3\sin \theta - 2 = 0$ is

Let $\theta \in [0, 4\pi ]$ satisfy the equation $(sin\, \theta + 2) (sin\, \theta + 3) (sin\, \theta + 4) = 6$ . If the sum of all the values of $\theta $ is of the form $k\pi $, then the value of $k$ is