We investigate the effects of an in-plane magnetic field on the weak antilocalization signature of near-surface quantum wells lacking bulk and inversion symmetry. The measured magnetoconductivity, which is conductivity as a function of the out-of-plane magnetic field, exhibits a strong anisotropy with respect to the direction of the in-plane magnetic field. The twofold symmetry of the observed magnetoanisotropy originates from the competition between Rashba and Dresselhaus spin-orbit couplings.