300 Followers problem

Geometry Level 4

$\prod_{r=1}^{5}\cos\left(\frac{(2r-1)\pi}{20}\right)+\prod_{r=0}^{3}\cos\left(\frac{2^{r}\pi}{15}\right)=$

This sum has the form $$\dfrac{1}{32}(A + \sqrt{B})$$ where $$A$$ and $$B$$ are integers. What is the value of $$A\times B?$$

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