We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $hat{theta} in (frac{pi}{2},frac{3pi}{2})$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path obtained by rewriting the equation as a generalised Monge-Amp`ere equation with mixed sign coefficients.
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