Consider a $2 \times 2$ unitary operator $U$.
There is a way to parametrize $U$, as
$$ U = e^{i \alpha} R_z(\phi) R_x(\theta) R_z(\lambda), $$
where $R_x, R_y$, and $R_z$ are $2 \times 2$ rotation matrices, given by
\begin{equation} R_t(\theta) = e^{-i \theta \sigma_t/2}, \end{equation}
where $\sigma_x, \sigma_y,$ and $\sigma_z$ are Pauli matrices.
Is there a similar way to parametrize a $3 \times 3$ unitary operator $U$?