# Haar Measures of $U(d)$ and $O(d)$

I'm trying to compute the Haar measures of finite unitary group $$U(d)$$ and finite orthogonal group $$O(d)$$. I've shown that both are compact groups. Most of computings I've seen base on Peter-Weyl Theorem but I'm not familiar with Lie Groups.

Is not possible to compute it by the exercise of Cohn's Measure Theory that takes place below :

If for each $$a$$ in $$G$$ the function $$u \mapsto \varphi(a\varphi^{−1}(u))$$ is the restriction to $$U$$ of an affine map $$L_a : \Bbb R^d \to \Bbb R^d$$, then the formula $$\mu(A)=\int_{\varphi(A)}|\det(L_{\varphi^{−1}(u)}|\lambda(du)$$ defines a left Haar measure on G. ($$\lambda$$ is Lebesgue measure on $$\Bbb R^d$$)

Can someone please explain how can I use this exercise for computing? Can I use Cayley transform as homeomorphism and do I have to use parametrization?