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

The general solution of

$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$

The general solution of $2 \cos ^2 x-2 \tan x+1=0$ is

$1+\sin x+\sin ^2 x+\sin ^3 x+\ldots \ldots+\infty=4+2 \sqrt{3}$ and $0