# What a Trigonometric Product!

Geometry Level 4

What is the sum of all positive integer values of $$n$$ that satisfy the equation

$\cos\Bigl(\frac{\pi}{n}\Bigr)\cos\Bigl(\frac{2\pi}{n}\Bigr)\cos\Bigl(\frac{4\pi}{n}\Bigr)\cos\Bigl(\frac{8\pi}{n}\Bigr)\cos\Bigl(\frac{16\pi}{n}\Bigr) =\frac{1}{32}\, ?$

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