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Mock AIME 2 2006-2007 Problems/Problem 10

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Problem

Find the number of solutions, in degrees, to the equation $\displaystyle \sin^{10}x + \cos^{10}x = \frac{29}{16}\cos^4 2x,$ where $\displaystyle 0^\circ \le x^\circ \le 2007^\circ.$

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