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**[SOLVED] Aime 2008 Ii 8**

## Homework Statement

Let [itex]a = \pi/2008[/itex]. Find the smallest positive integer n such that

[tex]2[\cos(a)\sin(a)+\cos(4a)\sin(2a)+\cos(9a)\sin(3a)+\cdots+\cos(n^2a)\sin(na)] [/tex]

is an integer.

## Homework Equations

[tex]\cos(a+b) = \cos a \cos b- \sin a \sin b[/tex]

[tex]\sin (a+b) = \sin a \cos b + \sin b \cos a[/tex]

## The Attempt at a Solution

Can someone give me a hint please? This should only require high school math. I am not sure if the identities above are useful here or if there is a totally different method needed.