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

Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { – \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$  is

(where $sgn(.)$ denotes signum function) –

Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta – cos\,2\theta  = 0$ and $2 \,cos^2\,\theta – 3\,sin\,\theta  = 0$ in the interval $[0, 2\pi ]$ is two.

Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta  – 3\,sin\,\theta  = 0$ in the interval $[0, \pi ]$ is two.

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

If $\sin 5x + \sin 3x + \sin x = 0$, then the value of $x$ other than $0$ lying between $0 \le x \le \frac{\pi }{2}$ is