Answer
$\theta=4.26+2k\pi$ and $\theta=5.16+2k\pi$
Six example solutions for $k=0,\pm1$:
$-2.02, -1.12, 4.26, 5.16, 10.54, 11.44$
Work Step by Step
Given $sin\theta=-0.9$, use a calculator,
we can find two $\theta$ values in $[0,2\pi],$ as $\theta=4.26, 5.16$
and the general solutions are $\theta=4.26+2k\pi$ and $\theta=5.16+2k\pi$
where $k$ is any integer. Six example solutions for $k=0,\pm1$:
$-2.02, -1.12, 4.26, 5.16, 10.54, 11.44$
