Number of distinct solutions of $\sec \theta +\tan \theta =\sqrt{3},0\le \theta \le 3\pi$ , is

$\frac{1+\sin \theta }{\cos \theta }=\sqrt{3}$

$\sin \theta +1=\sqrt{3}\cos \theta$

$\frac{\sqrt{3}}{2}\cos \theta -\frac{1}{2}\sin \theta =\frac{1}{2}$

$\cos \left(\theta +\frac{\pi }{6}\right)=\frac{1}{2}$

$\cos \left(\theta +\frac{\pi }{6}\right)=\cos \frac{\pi }{3}$

$\theta +\frac{\pi }{6}=2n\pi \pm \frac{\pi }{3}$

$\theta +\frac{\pi }{6}=2n\pi +\frac{\pi }{3}$   (or)  $\theta +\frac{\pi }{6}=2n\pi -\frac{\pi }{3}$

$\theta =2n\pi +\frac{\pi }{6}$   (or)  $\theta =2n\pi -\frac{\pi }{2}$

Number of solutions 3