The general solution of $\tan 3x = 1$ is

Consider the following lists:

$List-I$	$List-II$
$(I)$ $\{x \in[-\frac{2 \pi}{3}, \frac{2 \pi}{3}]: \cos x+\sin x=1\}$	$(P)$ has two elements
$(II)$ $\{x \in[-\frac{5 \pi}{18}, \frac{5 \pi}{18}]: \sqrt{3} \tan 3 x=1\}$	$(Q)$ has three elements
$(III)$ $\{x \in[-\frac{6 \pi}{5}, \frac{6 \pi}{5}]: 2 \cos (2 x)=\sqrt{3}\}$	$(R)$ has four elements
$(IV)$ $\{x \in[-\frac{7 \pi}{4}, \frac{7 \pi}{4}]: \sin x-\cos x=1\}$	$(S)$ has five elements
	$(T)$ has six elements

The correct option is:

The principal solutions of $\sqrt{3} \sec x + 2 = 0$ are

Find the value of $\theta$,if $|\tan \theta|=\tan \theta+\frac{1}{\cos \theta}$ and $\theta \in[0, 2\pi]-\{\pm \frac{\pi}{2}\}$

If $\alpha, \beta, \gamma$ and $\delta$ are the solutions of the equation $\tan \left( \theta + \frac{\pi}{4} \right) = 3 \tan 3\theta$,no two of which have equal tangents,then the value of $\tan \alpha + \tan \beta + \tan \gamma + \tan \delta$ is

The number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = -\frac{1}{2}$ for $\theta \in \left( 0, \frac{\pi}{2} \right)$ is: