$\text{cis } 75^\circ + \text{cis } 83^\circ + \text{cis } 91^\circ + \dots + \text{cis } 147^\circ$ 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.
I tried to use this site for geometric sequences, How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?. 

\begin{align}
   \text{cis }75^\circ +
      \text{cis }83^\circ +
      \text{cis }91^\circ + \dots +
      \text{cis }147^\circ
   &= \text{cis }75^\circ \left(
      1 +
      \text{cis }8^\circ +
      \text{cis }16^\circ + \dots +
      \text{cis }72^\circ \right)\\
   &= \text{cis }75^\circ \left(
      1 +
      \text{cis }8^\circ +
      (\text{cis }8^\circ)^2 + \dots +
      (\text{cis }8^\circ)^9 \right)\\
   &= \text{cis }75^\circ
      \dfrac{(\text{cis }8^\circ)^{10}-1}{\text{cis }8^\circ-1}\\
   &= \text{cis }75^\circ
      \dfrac{\text{cis }80^\circ-1}{\text{cis }8^\circ-1}\\
\end{align}
