# Stereographic projections and cross-ratios

Would anybody shed some light on question 2.11 in Wilson's Curved Spaces?

The numbers $p,q\in \hat{\mathbb{C}}$ are stereographic projections of points $P,Q$ on the unit sphere. The spherical distance between $P$ and $Q$ is $d$. The reader is asked to show that The cross-ratio of the four points $\{p,q,\bar{p}^{-1},\bar{q}^{-1}\}$ in some order is equal to $-\tan^2(d/2)$

(I am so sorry about the previous typos, I am typing on my phone.)

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