We report a measurement of time-dependent $CP$ violation parameters in ${B^0 to K_S^0 eta gamma}$ decays. The study is based on a data sample, containing ${772 times 10^6 Bbar{B}}$ pairs, that was collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We obtain the $CP$ violation parameters of ${{cal S} = -1.32 pm 0.77 {rm (stat.)} pm 0.36{rm (syst.)}}$ and ${{cal A} = -0.48 pm 0.41 {rm (stat.)} pm 0.07{rm (syst.)}}$ for the invariant mass of the $K_S^0 eta$ system up to 2.1 GeV/$c^2$.
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