The number of solutions of the equation $\sin 7 \theta-\sin 3 \theta=\sin 4 \theta$ that lie in the interval $(0, \pi)$, is

The smallest positive value of $x$ (in degrees) for which $\tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan (x) \tan \left(x-50^{\circ}\right)$ is

If the possible solution of the equation $2 \cos ^2 x+3 \sin x-3=0$ constitute two unequal angles of a triangle, then the third angle of that triangle is

If $\left|\sin x-\cos ^2 x\right| \geq\left|3-3 \sin x+\sin ^2 x\right|+4|\sin x-1|$, then $x=$