This is my first time in calculating this stuff so I would like to understand why the Haar measure on the group $U(2) / \left( U(1) \right)^2$ is deduced from:
$$ U^\dagger dU = -i \begin{pmatrix} \sin^2\phi & i\gamma \\ -i\bar{\gamma} & \cos^2\phi\end{pmatrix}, $$
with $\gamma=d\phi+i\sin\phi\cos\phi d\lambda$, to be
$$ \mu(U^\dagger dU)= \sin\phi\cos\phi d\phi d\lambda. $$
And mos importantly, how do I compute it? (Everyone says it is easy and trivial but no one actually does it.)