General Solution of a Trigonometric Equation

Solve the following trigonometric equation: $\cot x+cosecx=\sqrt{3}$.

Find the general solution of the following equation: 

$\sin 2x+\sin 4x+\sin 6x=0$

Find the general solution of the following equation:

$\sin x+\sin 3x+\sin 5x=0$

Find the general solution of the following equation:
$\sin 2x+\cos x=0$

Solve: $\cos \theta -\sin \theta =-1$

Solve: $\sqrt{3}\cos x-\sin x=1$

Find the general solution of $\cos 3x+\cos x-\cos 2x=0$.

Find the general solution of $\sin 2x-\sin 4x+\sin 6x=0$.

Find the general solution of $\cos 3x+\cos x-2\cos x=0$.

solve the following trigonometric equations :

$\sin 3x+\cos 2x=0$

solve the following trigonometric equations : 

$\tan x+\tan 2x+\tan x \tan 2x=1$

Solve the following trigonometric equations :

$3{\cos }^2\theta +7{\sin }^2\theta =4$

Find the general solution of $\sin x=-\frac{\sqrt{3}}{2}$.

Find the general solution of $\cos x=\frac{1}{2}$.

Find the general solution of the following trigonometric equations :

$\sin 3x=\frac{1}{\sqrt{2}}$

Find the general solution of $\cos \theta =-\frac{\sqrt{3}}{2}$.