JBMO-SL 2021 G5

Let $ABC$ be an acute scalene triangle with circumcircle $\omega$ . Let $P$ and $Q$ be interior points of the sides $AB$ and $AC$ , respectively, such that $PQ$ is parallel to $BC$ . Let $L$ be a point on $\omega$ such that $AL$ is parallel to $BC$ . The segments $BQ$ and $CP$ intersect at $S$ . The line $LS$ intersects $\omega$ at $K$ . Prove that $\angle BKP = \angle CKQ$ .

Proposed by Ervin Macić, Bosnia and Herzegovina