Euler's Formula on Complex Numbers

Let $n$ be a positive integer. Then it turns out $$\frac{1}{2} + \cos x + \cos 2x + \cdots + \cos nx = c\frac{\sin ((2n+1)x/2)}{\sin (x/2)}$$ for some constant $c$. What is $c$, rounded to the nearest tenth?

Source: http://math.stackexchange.com/questions/4961/interesting-results-easily-achieved-using-complex-numbers