The general solution of $\tan 3x = 1$ is

The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2x + \cos ^4 x + \sin ^4 x + \cos ^6 x + \sin ^6 x = 2$ in the interval $[0, 2\pi]$ is

If $\alpha$,$-\frac{\pi}{2} < \alpha < \frac{\pi}{2}$ is the solution of $4 \cos \theta + 5 \sin \theta = 1$,then the value of $\tan \alpha$ 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 $2\sin^2 \theta = 3\cos \theta$,where $0 \le \theta \le 2\pi$,then $\theta = $

For $n \in \mathbb{Z}$,the general solution of the trigonometric equation $\sin x - \sqrt{3} \cos x + 4 \sin 2x - 4 \sqrt{3} \cos 2x + \sin 3x - \sqrt{3} \cos 3x = 0$ is