Spin-orbit interaction is investigated in a dual gated InAs/GaSb quantum well. Using an electric field the quantum well can be tuned between a single carrier regime with exclusively electrons as carriers and a two-carriers regime where electrons and holes coexist. Spin-orbit interaction in both regimes manifests itself as a beating in the Shubnikov-de Haas oscillations. In the single carrier regime the linear Dresselhaus strength is characterized by $beta =$ 28.5 meV$AA$ and the Rashba coefficient $alpha$ is tuned from 75 to 53 meV$AA$ by changing the electric field. In the two-carriers regime the spin splitting shows a nonmonotonic behavior with gate voltage, which is consistent with our band structure calculations.
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