MathNet 2010 — Part 03 Question 178

Let $ABCDEFG$ be a regular heptagon. Suppose $P$, $Q$, $R$, $S$ are points on the line segments $AB$, $BC$, $CD$, $EF$, respectively, for which $BP = CQ = DR = FS = \frac{1}{3}$ are satisfied. Let $T$ be the point of intersection of the line segments $PR$ and $QS$. Find the value of $\angle PTS$.

Here by $XY$ we mean the length of the line segment $XY$.