Number of principal solution of the equation $tan \,3x - tan \,2x - tan\, x = 0$, is

The number of all possible values of $\theta$, where $0<\theta<\pi$, for which the system of equations

$ (y+z) \cos 3 \theta=(x y z) \sin 3 \theta $

$ x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z} $

$ (x y z) \sin 3 \theta=(y+2 z) \cos 3 \theta+y \sin 3 \theta$ have a solution $\left(\mathrm{x}_0, \mathrm{y}_0, \mathrm{z}_0\right)$ with $\mathrm{y}_0 \mathrm{z}_0 \neq 0$, is

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

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

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 set of all values of $\lambda$ for which the equation $\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda$