$ABCD$ 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 $\angle PCB$.
Problem
Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p1
Tags: geometry, rectangle, Equilateral, angles