NZ-NZMO 2022 Problem 1

$ABCD$ is a rectangle with side lengths $AB = CD = 1$ and $BC = DA = 2$ . Let $M$ be the midpoint of $AD$ . Point $P$ lies on the opposite side of line $MB$ to $A$ , such that triangle $MBP$ is equilateral. Find the value of $\angle PCB$ .