  In three-dimensional (3D) radiative transfer (RT) problems, the tensor
product quadratures are generally not optimal in terms of the number of
discrete ray directions needed for a given accuracy of the angular integration
of the radiation field. In this paper, we derive a new set of angular
quadrature rules that are more suitable for solving 3D RT problems with the
short- and long-characteristics formal solvers. These quadratures are more
suitable than the currently used ones for the numerical calculation of the
radiation field tensors that are relevant in the problem of the generation and
transfer of polarised radiation without assuming local thermodynamical
equilibrium (non-LTE). We show that our new quadratures can save up to about
30\,\% of computing time with respect to the Gaussian-trapezoidal product
quadratures with the same accuracy.
