PL-OM 2019 Problem 6

Denote by $\Omega$ the circumcircle of the acute triangle $ABC$ . Point $D$ is the midpoint of the arc $BC$ of $\Omega$ not containing $A$ . Circle $\omega$ centered at $D$ is tangent to the segment $BC$ at point $E$ . Tangents to the circle $\omega$ passing through point $A$ intersect line $BC$ at points $K$ and $L$ such that points $B, K, L, C$ lie on the line $BC$ in that order. Circle $\gamma_1$ is tangent to the segments $AL$ and $BL$ and to the circle $\Omega$ at point $M$ . Circle $\gamma_2$ is tangent to the segments $AK$ and $CK$ and to the circle $\Omega$ at point $N$ . Lines $KN$ and $LM$ intersect at point $P$ . Prove that $\sphericalangle KAP = \sphericalangle EAL$ .