HELP ME!! Precalc/Trig

I converted the question to an image, if you can answer this question that'll help a lot! Thanks!

Thank you, that is correct!

How did you come by those values Geno?

Let three of the $x_i$ be equal to 0, and let the remaining six be equal to $\frac{2 \pi}{3}.$ Then

$\cos x_1 + \cos x_2 + \dots + \cos x_9 = 3 \cos 0 + 6 \cos \frac{2 \pi}{3} = 3 + 6 \left( -\frac{1}{2} \right) = 0.$
Also, 

$\cos 3x_1 + \cos 3x_2 + \dots + \cos 3x_9 = 3 \cos 0 + 6 \cos 2 \pi = \boxed{9}.$
Since $\cos x \le 1$ for all $x,$ this is clearly the maximum.

Answer from AOPS's Alcumus.

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