Polar form of the sum of complex numbers $\operatorname{cis} 75 + \operatorname{cis} 83 + \ldots+ \operatorname{cis} 147$ 
The number $\operatorname{cis} 75 + \operatorname{cis} 83 + \operatorname{cis} 91 +\dots+ \operatorname{cis} 147$ is expressed in the form $r\operatorname{cis}(\theta)$, where $0\leq \theta< 360$. 
  Find $\theta$ in degrees

I'm having major trouble with this problem.

Hint: you want to evaluate $$e^{i(75\pi/180)}+e^{i(83\pi/180)}+e^{i(91\pi/180)}+\cdots +e^{i(147\pi/180)}.$$
This is a geometric series with common ratio $r=e^{i\frac{8\pi}{180}}.$
Now use the formula for the sum to $n$ terms of a geometric series: $$S_n=\frac{1-r^n}{1-r}.$$

Also, don't forget to convert back to degrees using 
$$\boxed{\theta^\circ =\theta^{\ \rm{rad}}\times \frac{180}{\pi}}.$$
