Playing With Cosines

Geometry Level 3

12x=cos(a)cos(2a)cos(3a)cos(999a)\large \dfrac1{2^x} = \cos (a) \cos(2a) \cos(3a) \cdots \cos(999a)

The equation above holds true for a=2π1999a = \dfrac{2\pi}{1999} . Find xx.

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