I have to solve following integration problem: $$I=\int_{-\pi}^{\pi} \eta^*(k) \partial_k \eta(k) dk$$ where $\eta^*(k)$ is conjugate of $\eta(k)$ and $$\eta(k)=\prod_{k=-\pi}^\pi\exp[{ia\cos(k)}]$$ with $a$ is constant. I am confused about $\prod_k$.
My attempt:
as $$\partial_k\eta(k)=i a \cos(k) \exp[{ia\cos(k)}]$$ so $$I=\int_{-\pi}^\pi \prod_{k=-\pi}^\pi ia \cos(k) dk$$ How to deal with product over $k$?