Answer
The corresponding values of $\theta$ are $$\{60^\circ,210^\circ,240^\circ,310^\circ\}$$
Work Step by Step
1) The question asks for solutions over the interval $[0^\circ, 360^\circ)$, meaning that
$$\theta\in[0^\circ,360^\circ)$$
or $$0^\circ\le\theta\lt360^\circ$$
2) Now from also the question, your work leads to $$3\theta=180^\circ,630^\circ,720^\circ,930^\circ$$
To find corresponding values of $\theta$ from $3\theta$, we divide both sides by $3$
$$\theta=60^\circ,210^\circ,240^\circ,310^\circ$$
3) Finally, it is crucial to compare the values of $\theta$ in 2) with the range found in 1).
We see that all four values of $\theta=60^\circ,210^\circ,240^\circ,310^\circ$ fit in the range of $\theta\in[0^\circ,360^\circ)$. None would be eliminated as a result.
The corresponding values of $\theta$ are $$\{60^\circ,210^\circ,240^\circ,310^\circ\}$$
