Point $D$ is on side $\overline{BC}$ of triangle $ABC.$  If $\angle CAD = \angle BAD = 60^\circ,$ $AC = 3,$ and $AB = 6,$ then find $AD.$
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Point $D$ is on side $\overline{BC}$ of triangle $ABC.$  If $\angle CAD = \angle BAD = 60^\circ,$ $AC = 3,$ and $AB = 6,$ then find $AD.$
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Point $D$ is on side $\overline{BC}$ of triangle $ABC.$  If $\angle CAD = \angle BAD = 60^\circ,$ $AC = 3,$ and $AB = 6,$ then find $AD.$
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