How to show the following summation is true?

[Bishop556]

I need to prove that the following summation is true:

∑(-1)^n * cos(nx) / n^2 = (3x^2 - π^2)/12

How would I tackle this problem?

 

[Svein]

Hint: $\sum_{n=1}^{\infty}\frac{1}{n^{2}}=\frac{\pi^{2}}{6}$