Answer
$90^\circ, 270^\circ$
Work Step by Step
1. Use the identify $sin^2\theta+cos^2\theta=1$, we have $1-cos^2\theta=cos^2\theta +1$, thus $cos^2\theta=0$ and $cos\theta=0$
2. For $\theta\in[0^\circ,360^\circ)$, we can find $\theta=90^\circ, 270^\circ$
