## Last complex trig question...hopefully! =p

Sum: (where Q is theta)
sin Q - 1/3sin2Q + 1/9sin3Q - 1/27sin4Q...

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

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

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

And according to the answers numerator should be e^Qi...
Why is this :S?