A flavour-tagged decay-time-dependent amplitude analysis of Bs0 → (K+π−)(K−π+) decays is presented in the K±π∓ mass range from 750 to 1600MeV/c2. The analysis uses pp collision data collected with the LHCb detector at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0 fb−1. Several quasi-two-body decay modes are considered, corresponding to K±π∓ combinations with spin 0, 1 and 2, which are dominated by the K0*(800)0 and K0*(1430)0, the K*(892)0 and the K2*(1430)0 resonances, respectively. The longitudinal polarisation fraction for the Bs0→K∗(892)°K¯∗(892)0 decay is measured as fL = 0.208 ± 0.032 ± 0.046, where the first uncertainty is statistical and the second is systematic. The first measurement of the mixing-induced CP-violating phase, ϕsdd¯, in b→ dd¯ s transitions is performed, yielding a value of ϕsdd¯=−0.10±0.13(stat)±0.14 (syst) rad.