Is there a closed form product of $\cos(kx)$?

Question

Is there a closed form for $$\prod_{k=1}^n \cos(kx)$$ where $n>0$ is an integer?

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This was proposed as $\prod_{k=1}^n a^k+\overline{a^k}$ where $a$ is a complex number, in the book of Claude Deschamps and Andre Warusfel (a French book).