Answer
$\pi/3+2k\pi$, $2\pi/3+2k\pi$, $4\pi/3+2k\pi$, $5\pi/3+2k\pi$
Work Step by Step
$\tan \theta-3\cot \theta=0$
$\frac{\sin\theta}{\cos \theta}-3*\frac{\cos \theta}{\sin \theta}=0$
Multiplying both sides by $\sin\theta\cos\theta$:
$\sin^2\theta-3\cos^2\theta=0$
$\sin^2\theta+\cos^2\theta-4\cos^2\theta=0$
$1-4\cos^2\theta=0$
$4\cos^2\theta=1$
$\cos^2\theta=1/4$
$\cos\theta=\pm1/2$
If $\cos \theta=1/2$, then $\theta=\pi/3+2k\pi$ or $\theta=5\pi/3+2k\pi$.
If $\cos \theta=-1/2$, then $\theta=2\pi/3+2k\pi$ or $\theta=4\pi/3+2k\pi$.
