Question 25In the following diagram, $P_1,P_2,\ldots,P_8$ are points on $\triangle ABC$ such that $$|AP_1|=|AP_8|=|P_iP_{i+1}|,\qquad\text{for all }i=1,2,\ldots,7.$$ What is the value (in degrees) of $\angle BAC$?
