A classical mechanics problem by Tai Ching Kan

I have a uniform lamina of mass \(2m\) in the shape of a regular hexagon, centre \(O\) and vertices \(ABCDEF\), clockwise in that order. I attach the following masses to the lamina: \(2m\) at vertex \(C\), \(m\) at the midpoint of \(EF\), and \(3m\) at the midpoint of \(OB\).

When I hang the lamina at \(A\) so that it can rotate freely, find the angle that \(AB\) makes with the downward vertical, giving your answer in degrees to 3 decimal places.

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