I'm having trouble with this series
$$ \sum_{n=1}^\infty \left(\frac{\dot{\alpha}}{\alpha}i+2\dot{\theta}\right)\alpha^ne^{in\theta} + \overline{\left(\frac{\dot{\alpha}}{\alpha}i+2\dot{\theta}\right)\alpha^ne^{in\theta}} = - \dot{\theta}. $$
$\alpha$ is complex but $\theta$ is not.
I'd like to find an expression for $\dot{\alpha}$, my fourier series knowledge is a little rusty, so if anyone would give a hint, it would be much appreciated.