Let $w = \frac { \sqrt { 3 } + \mathrm { i } } { 2 }$ and $P = \left\{ w ^ { n } : n = 1,2,3 , \ldots \right\}$. Further $H _ { 1 } = \left\{ \mathrm { z } \in \mathbb { C } : \operatorname { Re } z > \frac { 1 } { 2 } \right\}$ and $H _ { 2 } = \left\{ \mathrm { z } \in \mathbb { C } : \operatorname { Re } z < \frac { - 1 } { 2 } \right\}$, where $\mathbb { C }$ is the set of all complex numbers. If $z _ { 1 } \in P \cap H _ { 1 }$, $z _ { 2 } \in P \cap H _ { 2 }$ and $O$ represents the origin, then $\angle z _ { 1 } O z _ { 2 } =$
(A) $\frac { \pi } { 2 }$
(B) $\frac { \pi } { 6 }$
(C) $\frac { 2 \pi } { 3 }$
(D) $\frac { 5 \pi } { 6 }$