for 0<= θ <=360, solve (sin θ +1)(2cos θ -1)=0
You could...but its best if you try to memorize these values from the unit circle: Unit circle - Wikipedia, the free encyclopedia
In our case, $\displaystyle \sin^{-1}\left(-1\right)$ has only one value in the specified interval for $\displaystyle \theta$, and its $\displaystyle \theta=270^{\circ}$
However, $\displaystyle \cos^{-1}\left(\tfrac{1}{2}\right)$ has two solutions in the given interval for $\displaystyle \theta$. They are $\displaystyle \theta_1=60^{\circ}$ and $\displaystyle \theta_2=300^{\circ}$.
Your final answer to the original question is all three values for $\displaystyle \theta$.
Does this make sense?