If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are

If $\cos \theta + \cos 7\theta + \cos 3\theta + \cos 5\theta = 0$, then $\theta $

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

General value of $\theta $ satisfying the equation ${\tan ^2}\theta + \sec 2\theta - = 1$ is

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

Number of solution $(s)$ of equation $cosec\, \theta -cot \,\theta = 1$ in $[0,2 \pi]$ is-