Even though your method is the simplest, it assumes that the answer is in the first quadrant, which it might not be. Once the OP has found $\displaystyle \displaystyle \begin{align*} \tan{\theta} \end{align*}$ for $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$ in the first quadrant, he/she needs to realise that $\displaystyle \displaystyle \begin{align*} \tan{\theta} \end{align*}$ is also positive in the third quadrant, and in the third quadrant, $\displaystyle \displaystyle \begin{align*} \sin{\theta} \end{align*}$ is negative.
So there are actually two possibilities, the positive and the negative of what the OP finds using your method