I'm looking for a hint on how to prove that

$\displaystyle \sum \limits _{k=1}^n \cos \left[(2k-1)\theta\right]=\dfrac{\sin \left(2n \theta\right) }{2\sin \theta}$

I know I'm on here a lot but I really have no one to go to for guidance and am trying to learn this material on my own from the text book. Thank you for being patient with me so far and for being so helpful.