This paper proposes a novel methodology to derive nonlinear solutions of an indeterminate DSGE model in which the decision rules are affected by sunspot shocks. We apply the method to an expectations-driven liquidity trap---a liquidity trap that arises because of the zero lower bound constraint on the nominal interest rate and the de-anchoring of economic agents' expectations---and find that the model dynamics exhibit significant nonlinearity. Such nonlinearity arises because the zero lower bound ceases to bind once the inflation rate rises because of a temporary increase in inflation expectations.