Mock AIME 1 2006-2007 Problems/Problem 3

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3. Let $\triangle ABC$ have $BC=\sqrt{7}$, $CA=1$, and $AB=3$. If $\angle A=\frac{\pi}{n}$ where $n$ is an integer, find the remainder when $n^{2007}$ is divided by $1000$.

Mock AIME 1 2006-2007