Chebyshev polynomial practice: medium hard product

Geometry Level 2

n=12016sec(nπ2017) \large \displaystyle \prod_{n=1}^{2016} \sec\left(\dfrac{n\pi}{2017}\right)

Evaluate the product above.

Given that the above is equal to aba^b where a is a prime number, find a+ba+b.

Inspired by this problem when I solved it in 3 steps... All of which were wrong, but somehow I got the right answer.

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