2. As shown in the figure, $M, N$ are points on the sides $AD, BC$ of the spatial quadrilateral $ABCD$. $AB=1, \frac{AM}{AD}=\frac{BN}{BC}=\frac{1}{3}$, the angle between $MN$ and $AB$ is equal to the angle between $MN$ and $CD$, then $CD$ equals $\qquad$ .
2. 2 Detailed Explanation: Connect $B D$, and take point $E$ on $B D$ such that $\frac{B E}{B D}=\frac{1}{3}$, then connect $M E, N E$. Thus, $M E \parallel A B, N E \parallel C D$. From the given conditions, $\angle E M N=\angle E N M$, so $D C=3 N E=3 M E=2 A B=2$.