Answer
$\theta=-1.47+k\pi$
Six example solutions for $k=0,\pm1,\pm2,3$:
$-7.75, -4.61, -1.47, 1.67, 4.81, 7.95$
Work Step by Step
Given $tan\theta=-10$, use a calculator,
we can find one $\theta$ values in $[-\frac{\pi}{2},\frac{\pi}{2}],$ as $\theta=-1.47$
and the general solutions are $\theta=-1.47+k\pi$
where $k$ is any integer. Six example solutions for $k=0,\pm1,\pm2,3$:
$-7.75, -4.61, -1.47, 1.67, 4.81, 7.95$
