 Weyl integration formula for SU(2)

For a class function on SU(2) and normalized Haar measure, the displayed formula reduces a group integral to its conjugacy-class angle. The weight follows by identifying SU(2) with the unit sphere in four real dimensions: writing a unit quaternion as $\cos \theta +\mathbf{n}\sin \theta$ gives spherical volume proportional to ${\sin }^2\theta d\theta d\mathbf{n}$. Since ${\int }_0^{\pi }{\sin }^2\theta d\theta =\pi /2$, normalization gives $2/\pi$.