Question: simplify real trig expression

A reddit user posted an interesting question:

http://www.reddit.com/r/math/comments/1eyx0f/help_with_simplifying_in_maple/

The problem is how to simplify, e.g. 2/3*37^(1/2)*sin(1/6*Pi+1/3*arccos(55/1369*37^(1/2)))+2/3 to 4.  I tried a few things and got nowhere.  Any suggestions?

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