Answer
$0, 1.911, \pi, 4.373$
Work Step by Step
Step 1. $-3cos(\frac{\pi}{2}-\theta)=tan(\theta) \longrightarrow -3sin(\theta)=sin(\theta)/cos(\theta)$
Thus we have $sin(\theta)=0$ or $cos(\theta)=-\frac{1}{3}$
Step 2. For $sin(\theta)=0$, we have $\theta=k\pi$
Step 3. For $cos(\theta)=-\frac{1}{3}$, we have $\theta=2k\pi+cos^{-1}(-\frac{1}{3})\approx2k\pi+1.911$ and $\theta=2k\pi+2\pi-cos^{-1}(-\frac{1}{3})\approx2k\pi+4.373$
Step 4. Within $[0,2\pi)$, we have $\theta=0, 1.911, \pi, 4.373$
