  This work focuses on angular values of nonautonomous dynamical systems which
have been introduced for general random and (non)autonomous dynamical systems
in a previous publication [W.-J. Beyn, G. Froyland, and T. H\"uls, SIAM J.
Appl. Dyn. Syst., 21 (2022), pp. 1245--1286]. The angular value of dimension
$s$ measures the maximal average rotation which an $s$-dimensional subspace of
the phase space experiences through the dynamics of a discrete-time linear
system. Our main results relate the notion of angular value 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 maximizing
over all subspaces, it suffices to maximize over 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 systems of dimension up to 4 and demonstrate its efficiency to
detect the fastest rotating subspace even if it is not dominant under the
forward dynamics.
