Answer
$\sin \theta=k\pi$
Work Step by Step
Because of the Pythagorean identity $\sin^2\theta+\cos^2\theta=1$, we can rewrite $\sin \theta+\sin^2\theta+\cos^2\theta=1$ as $\sin \theta+1=1$, which means $\sin \theta=0$. This is true whenever the y-value of $\theta$ on the unit circle is 0, which happens at $\theta=k\pi$.
