A model-dependent amplitude analysis of the decay B0 → D(KS0π+π−)K∗0 is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb−1, recorded at √s=7 and 8 TeV by the LHCb experiment. The CP violation observables x± and y±, sensitive to the CKM angle γ, are measured to bex−=−0.15±0.14±0.03±0.01,y−=0.25±0.15±0.06±0.01,x+=0.05±0.24±0.04±0.01,y+=−0.65−0.23+0.24±0.08±0.01, where the first uncertainties are statistical, the second systematic and the third arise from the uncertainty on the D → KS0π+π− amplitude model. These are the most precise measurements of these observables. They correspond to γ = (80−22+21)° and rB0=0.39±0.13, where rB0 is the magnitude of the ratio of the suppressed and favoured B0 → DK+π− decay amplitudes, in a Kπ mass region of ±50 MeV around the K*(892)0 mass and for an absolute value of the cosine of the K*0 decay angle larger than 0.4.[Figure not available: see fulltext.]