  This work continues the investigation of the previously defined angular
values for linear nonautonomous dynamical systems in finite dimensions. The
$s$-th angular value measures the maximal average rotation which the dynamics
exerts on $s$-dimensional subspaces. Our main theorem relates the angular
values to the well-known dichotomy (or Sacker-Sell) spectrum and its associated
spectral bundles. In particular, we prove a reduction theorem which shows that
instead of general subspaces it suffices to consider so-called trace spaces
which have their basis in the spectral fibers. The reduction leads to an
algorithm for computing angular values of dimensions one and two. We apply the
algorithm to several examples of dimension up to $4$, including a system of
coupled oscillators.
