# Is this a Trigonometry Problem or a Number Theory Problem?

$\large \mathcal{S} = \sum_{a \in \mathcal{P}} \cos \left( 2 \pi \dfrac{a}{1001} \right)$

Let us a define a set $\large \mathcal{P}$ which contains all the natural numbers less than or equal to 1001 and are coprime to 1001.

Evaluate the value of $\mathcal{S}$.

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