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, has only one value in the specified interval for , and its
However, has two solutions in the given interval for . They are and .
Your final answer to the original question is all three values for .
Does this make sense?