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

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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