Let $w=\frac{\sqrt{3}+i}{2}$ and $P=\left\{w^n: n=1,2,3, \ldots.\right\}$. Further $H_1=\left\{z \in C: \operatorname{Re} z>\frac{1}{2}\right\}$ and $H_2=\left\{z \in C: \operatorname{Re} z<-\frac{1}{2}\right\}$, where C is the set of all complex numbers. If $\mathrm{z}_1 \in \mathrm{P} \cap \mathrm{H}_1, \mathrm{z}_2 \in \mathrm{P} \cap \mathrm{H}_2$ and O represents the origin, then $\angle \mathrm{z}_1 O \mathrm{z}_2=$