Question 18
Let $ABCDEFGH$ be an equilateral octagon with $\angle A \cong \angle C \cong \angle E \cong \angle G$ and $\angle B \cong \angle D \cong \angle F \cong \angle H$. If the area of $ABCDEFGH$ is three times the area of $ACEG$, then $\sin B$ can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100m+n$.