The equation $3\cos x + 4\sin x = 6$ has

The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is

If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is

The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is

The equation $\sin x + \sin y + \sin z = - 3$ for $0 \le x \le 2\pi ,$ $0 \le y \le 2\pi ,$ $0 \le z \le 2\pi $, has

If $\sin 2\theta = \cos 3\theta $ and $\theta $ is an acute angle, then $\sin \theta $ is equal to