Sum of cosines

Geometry Level 5

A=cos(13π20)+cos(21π20)+cos(29π20)+cos(37π20)A=\cos\left(\frac{13\pi}{20}\right) +\cos\left(\frac{21\pi}{20}\right) +\cos\left(\frac{29\pi}{20}\right) +\cos\left(\frac{37\pi}{20}\right)

Find the value of 1000A\lfloor 1000A \rfloor.


Notation: \lfloor \cdot \rfloor denotes the floor function.

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