I have a rectangle of side lengths $x,y$ projected onto a sphere, with arc lengths $x',y'$ and arc angles $\phi,\theta$. If I have $x,y$, how can I derive $\phi,\theta$? I was able to accomplish the opposite via $x = r\cdot\theta\cos\frac\phi2$ and $y = r\cdot\phi\cdot\cos\frac\theta2$
