Triangle Trigonometry and Vectors · Superchallenge problem

Right triangle $ABC$ has its right angle at $C$, with $CA=2$ and $CB=4$. The median from $A$ goes to the midpoint of $\overline{BC}$, and the median from $B$ goes to the midpoint of $\overline{AC}$. Find the tangent of the acute angle between these two medians.