  We exploit the high-symmetry spin state obtained for equal Rashba and linear
Dresselhaus interactions to derive a closed-form expression for the weak
localization magnetoconductivity -- the paradigmatic signature of spin-orbit
coupling in quantum transport. The small parameter of the theory is the
deviation from the symmetry state introduced by the mismatch of the linear
terms and by the cubic Dresselhaus term. In this regime, we perform quantum
transport experiments in GaAs quantum wells. Top and back gates allow
independent tuning of the Rashba and Dresselhaus terms in order to explore the
broken-symmetry regime where the formula applies. We present a reliable
two-step method to extract all parameters from fits to the new expression,
obtaining excellent agreement with recent experiments. This provides
experimental confirmation of the new theory, and advances spin-orbit coupling
towards a powerful resource in emerging quantum technologies.
