Measurement of the time-dependent CP asymmetries in B0-->K(S)(0)rho(0)gamma decays.

We report the first measurement of time-dependent CP asymmetry in B(0)-->K(S)(0)rho(0)gamma decays based on 657 x 10(6) BB pairs collected with the Belle detector at the KEKB asymmetric-energy collider. We measure the CP-violating parameter S_{K_{S};{0}rho;{0}gamma}=0.11+/-0.33(stat)-0.09+0.05(syst) from a signal of 212+/-17 events. We also obtain the effective direct CP-violating parameter A{eff}=0.05+/-0.18(stat)+/-0.06(syst) for mK(S)0pi+pi- <1.8 GeV/c(2) and 0.6 GeV/c(2)