CMO 2021 Problem 4

In acute triangle $ABC (AB>AC)$ , $M$ is the midpoint of minor arc $BC$ , $O$ is the circumcenter of $(ABC)$ and $AK$ is its diameter. The line parallel to $AM$ through $O$ meets segment $AB$ at $D$ , and $CA$ extended at $E$ . Lines $BM$ and $CK$ meet at $P$ , lines $BK$ and $CM$ meet at $Q$ . Prove that $\angle OPB+\angle OEB =\angle OQC+\angle ODC$ .