AMC 12 2022a Problem 12

Let $M$ be the midpoint of $\overline{AB}$ in regular tetrahedron $ABCD$. What is $\cos(\angle CMD)$?

$\textbf{(A) } \frac14 \textbf{(B) } \frac13 \textbf{(C) } \frac25 \textbf{(D) } \frac12 \textbf{(E) } \frac{\sqrt{3}}{2}$