Let $ABCD$ be a rectangle with $AD=2AB$ . $G,H$ are on $AD$ and $BC$ repectively such that $AG:GD=BH:HC=3:1$ . Let $GH$ be the minor arc with midpoint $K$ of the cicumcircle of $\triangle$$GHD$. $DK$ intersects $BC$ at $M$ . Find $\angle$$DMC$.