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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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