  We show that the empirical eigenvalue measure for sum of $d$ independent Haar
distributed $n$-dimensional unitary matrices, converge for $n \to \infty$ to
the Brown measure of the free sum of $d$ Haar unitary operators. The same
applies for independent Haar distributed $n$-dimensional orthogonal matrices.
As a byproduct of our approach, we relax the requirement of uniformly bounded
imaginary part of Stieltjes transform of $T_n$ that is made in [Guionnet,
Krishnapur, Zeitouni; Theorem 1].
