Let $ABCDEFG$ be a regular heptagon with center $O$.  Let $M$ be the centroid of triangle $ABD$.  Find $\cos^2 \angle GOM$.
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<|im_start|>user
Let $ABCDEFG$ be a regular heptagon with center $O$.  Let $M$ be the centroid of triangle $ABD$.  Find $\cos^2 \angle GOM$.
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user
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Let $ABCDEFG$ be a regular heptagon with center $O$.  Let $M$ be the centroid of triangle $ABD$.  Find $\cos^2 \angle GOM$.
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