  We derive a closed-form expression for the weak localization (WL) corrections
to the magnetoconductivity of a 2D electron system with arbitrary Rashba
$\alpha$ and Dresselhaus $\beta$ (linear) and $\beta_3$ (cubic) spin-orbit
interaction couplings, in a perpendicular magnetic field geometry. In a system
of reference with an in-plane $\hat{z}$ axis chosen as the high spin-symmetry
direction at $\alpha = \beta$, we formulate a new algorithm to calculate the
three independent contributions that lead to WL. The antilocalization is
counterbalanced by the term associated with the spin-relaxation along
$\hat{z}$, dependent only on $\alpha - \beta$. The other term is generated by
two identical scattering modes characterized by spin-relaxation rates which are
explicit functions of the orientation of the scattered momentum. Excellent
agreement is found with data from GaAs quantum wells, where in particular our
theory correctly captures the shift of the minima of the WL curves as a
function of $\alpha/\beta$. This suggests that the anisotropy of the effective
spin relaxation rates is fundamental to understanding the effect of the SO
coupling in transport.
