Number of solutions of equation $secx = 1 + cosx + cos^2x + ........ \infty$ in $x \in [-50 \pi, 50 \pi]$ is -

If $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, then the general value of $\theta $ is

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

Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$

The smallest positive root of the equation $tanx\,  -\,  x = 0$ lies on