Let $PSL(2,mathbb{R})$ be the **Projective Special Linear Group** and $PSO(2)$ be the **Projective Special Orthogonal Group**.

It is well-known that $PSL(2,mathbb{R})/PSO(2)$ can be identified with the **upper half-plane** $mathbb{H}$.

Let $g,h$ be two elements of $PSL(2,mathbb{R})$, How can the **hyperbolic distance** between $gPSO(2)$ and $hPSO(2)$ be computed?