Answer
$0.20+2k\pi$, $2.94+2k\pi$
Work Step by Step
$\begin{align}
5\sin\theta-1&=0\\
5\sin\theta&=1\\
\sin\theta&=\frac{1}{5}
\end{align}$
Since $\sin \theta$ is positive in the first and second quadrants, the only values of $\theta$ between $0$ and $2\pi$ that satisfy the equation are $0.20$ and $\pi-0.20\approx 2.94$.
Since $\sin \theta$ is a periodic function with period $2\pi$, we can add or subtract any multiple of $2\pi$ from $0.20$ or $2.94$ and the equation would still be satisfied.
So the answers are $0.20+2k\pi$ and $2.94+2k\pi$ for any integer $k$.
