Sum: (where Q is theta)

sin Q - 1/3sin2Q + 1/9sin3Q - 1/27sin4Q...

Okey, so using Geometric summation of an infinite series =) i get

$\displaystyle

\frac{e^(Qi)}{1 - e^(-Qi)}

$

But when i 'realise' / rationalise it i get the numerator as $\displaystyle e^Qi - \frac{1}{3}$

And according to the answers numerator should be e^Qi...

Why is this :S?