Chebyshev polynomial practice: medium hard product

Geometry Level 3

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

Evaluate the product above.

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

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