  Shubnikov-de Haas (SdH) oscillations have served as a paradigmatic
experimental probe and tool for extracting key semiconductor parameters such as
carrier density, effective mass, Zeeman splitting with g-factor $g^*$, quantum
scattering times and spin-orbit (SO) coupling parameters. Here, we derive for
the first time an analytical formulation for the SdH oscillations in 2D
electron gases (2DEGs) with simultaneous Rashba, Dresselhaus, and Zeeman
interactions. Our analytical and numerical calculations allow us to extract
both Rashba and Dresselhaus SO coupling parameters, carrier density, quantum
lifetimes, and also to understand the role of higher harmonics in the SdH
oscillations. More importantly, we derive a simple condition for the vanishing
of SO induced SdH beatings for all harmonics in 2DEGs: $\alpha/\beta=
[(1-\tilde \Delta)/(1+\tilde \Delta)]^{1/2}$, where $\tilde \Delta$ is a
material parameter given by the ratio of the Zeeman and Landau level splitting.
We also predict beatings in the higher harmonics of the SdH oscillations and
elucidate the inequivalence of the SdH response of Rashba-dominated
($\alpha>\beta$) vs Dresselhaus-dominated ($\alpha<\beta$) 2DEGs in
semiconductors with substantial $g^*$. We find excellent agreement with recent
available experimental data of Dettwiler ${\it et\thinspace al.}$ Phys. Rev. X
$\textbf{7}$, 031010 (2017), and Beukman ${\it et\thinspace al.}$, Phys. Rev. B
$\textbf{96}$, 241401 (2017).
