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

**Number Theory**Level 5

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

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 \(\mathcal{S}\).