  In a previous paper (Lathouwers and Perk\'o, 2019) we have developed an
efficient angular multigrid preconditioner for the Boltzmann transport equation
with forward-peaked scatter modeled by the Fokker-Planck approximation. The
discretization was based on a completely discontinuous Galerkin finite element
scheme both for space and angle. The scheme was found to be highly effective on
isotropically and anisotropically refined angular meshes. The purpose of this
paper is to extend the method to non-Fokker-Planck models describing the
forward scatter by general Legendre expansions. As smoother the standard source
iteration is used whereas solution on the coarsest angular mesh is effected by
a special sweep procedure that is able to solve this problem with highly
anisotropic scatter using only a small number of iterations. An efficient
scheme is obtained by lowering the scatter order in the multigrid
preconditioner. A set of test problems is presented to illustrate the
effectivity of the method, i.e. in less iterations than the single-mesh case
and more importantly with reduced computational effort.
