Consider the Earth to be a perfect sphere of radius $\text{R}$. Then the surface area of the region, enclosed by the $60^{\circ} \mathrm{N}$ latitude circle, that contains the north pole in its interior is $\_\_\_\_\_\_$.
- $(2-\sqrt{3}) \pi R^{2}$
- $\frac{(\sqrt{2}-1) \pi R^{2}}{2}$
- $\frac{2 \pi R^{2}}{3}$
- $\frac{(2+\sqrt{3}) \pi R^{2}}{8 \sqrt{2}}$