Please shed some light on how I can start the proof.
$$\sin{\alpha} +r\sin({\alpha + \phi}) + ... + r^n\sin({\alpha} + n\phi) \\= {\frac{\sin{\alpha}-r\sin({\alpha} - {\phi}) - r^{n+1}\sin((n+1){\phi} + {\alpha}) + r^{n+2}\cos(n{\phi} + {\alpha})}{1-2r\cos{\phi} + r^2}}.$$