Another way to express $\text{cis } 75^\circ + \text{cis } 83^\circ + \text{cis } 91^\circ + \dots + \text{cis } 147^\circ$ The number
$$\text{cis } 75^\circ + \text{cis } 83^\circ + \text{cis } 91^\circ + \dots + \text{cis } 147^\circ$$ is expressed in the form $r \, \text{cis } \theta$, where $0 \le \theta < 360^\circ$. Find $\theta$ in degrees.

Hint: $\text{cis}\ \theta=\cos \theta+i \sin \theta$

Edit:
I simplified the expression down to$$\frac{\text{cis} \ 75^\circ \sin 40^\circ \ \text{cis} \ 40^\circ }{\sin 4^\circ \ \text{cis} \ 4^\circ}.$$
What should I do now?

\begin{align}
&\text{cis} 75 ^\circ+\text{cis} 83 ^{\circ}+\ldots + \text{cis}147^\circ \\
&= \text{cis} 75^{\circ}(1+\text{cis}8 ^\circ+\ldots+\text{cis}72^{\circ}) \\
\end{align}
Using the geometric series formula, the answer is the same as:
The expression $\frac{(\text{cis}\ 75^\circ)(\text{cis}\ 80^\circ−1)}{\text{cis}\ 8^\circ−1}$ can be written as $r\ \text{cis}\ \theta$. 
