AMO 2021 – Junior College (Grades 11–12) Question 21

In rectangle $ABCD$, $AB=2$ cm and $BC=2\sqrt3$ cm. As shown, $M$ lies in the interior of $AD$, $N$ lies in the interior of $BC$, and $AM=CN$. Point $P$ lies on $CD$. When $MP+NP$ is minimized, find $\tan^2\angle MPN$.