Distance between two cities on Earth

Be careful. All angles are measured in radians. In accord with the question $\phi$ means the latitude ($=\frac{\pi}{2}-\text{polar angle}$) and $\theta$ means the longitude (azimuth angle).

If one considers the Earth being a ball, the shortest path is: $$ d=R\arccos(\sin\phi_1\sin\phi_2+\cos\phi_1\cos\phi_2\cos(\theta_2-\theta_1)), $$ the argument of $\arccos$ being the scalar product of unit vectors directed from the Earth center to the points on the surface.

The "naive path" for $\phi_1=\phi_2\equiv\phi$ has length: $$ d^*=R(\theta_2-\theta_1)\cos\phi. $$

In the last expression $0\le\theta_2-\theta_1\le\pi$ is assumed. Generally $\arccos\cos(\theta_2-\theta_1)$ can be used instead.

Use that chord length and the Earth's radius to determine the arc length around the curved path.