Let $d$ be a metric on the unit circle $$S=\lbrace(\cos\theta, \sin\theta): 0 \le \theta < 2\pi\rbrace$$ defined by $$d(x_{1},x_{2})=|\theta_{1}-\theta_{2}|$$ where
$$\begin{align*} x_{1}&=(\cos\theta_{1}, \sin\theta_{1})\\ x_{2}&=(\cos\theta_{2}, \sin\theta_{2}). \end{align*} $$
What are the open sets in $S$?
I know the definition of open sets however I am unable to think of one in this case.