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We present a first-principles study of the electronic properties of CuIn(S,Se)2 (CIS) using state-of-the-art self-consistent GW and hybrid functionals. The calculated band gap depends strongly on the anion displacement u, an internal structural parameter that measures lattice distortion. This contrasts with the observed stability of the band gap of CIS solar panels under operating conditions, where a relatively large dispersion of values for u occurs. We solve this apparent paradox considering the coupled effect on the band gap of copper vacancies and lattice distortions. The correct treatment of d electrons in these materials requires going beyond density functional theory, and GW self-consistency is critical to evaluate the quasiparticle gap and the valence band maximum.