Suppose \[sin^{3} x \sin 3x = \displaystyle \sum_{m=0}^{n} c_{m} \cos mx \] is an identity in \(x\) where \(c_{0} , c_{1} , ... , c_{n}\) are constants, and \(c_{n}≠0\). Then find the value of n.

This problem is part of the set Trigonometry.

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