Microparticle adsorption and self-assembly at fluid interfaces are strongly affected by the particle three-phase contact angle θ. On the single-particle level, θ can be determined by several techniques, including colloidal-probe AFM, the gel-trapping technique (GTT) and the freeze-fracture shadow-casting (FreSCa) method. While GTT and FreSCa provide contact angle distributions measured over many particles, colloidal-probe AFM measures the wettability of an individual (specified) particle attached onto an AFM cantilever. In this paper, we extract θ for smooth microparticles through the analysis of force-distance curves upon particle approach and retraction from the fluid interface. From each retraction curve, we determine: (i) the maximal force, Fmax; (ii) the detachment distance, Dmax; and (iii) the work for quasistatic detachment, W. To relate Fmax, Dmax and W to θ, we developed a detailed theoretical model based on the capillary theory of flotation. The model was validated in three different ways. First, the contact angles, evaluated from Fmax, Dmax and W, are all close in value and were used to calculate the entire force-distance curves upon particle retraction without any adjustable parameters. Second, the model was successfully applied to predict the experimental force-distance curve of a truncated sphere, whose cut is positioned below the point of particle detachment from the interface. Third, our theory was confirmed by the excellent agreement between the particle contact angles obtained from the colloidal-probe AFM data and the ensemble-average contact angles measured by both GTT and FreSCa. Additionally, we devised a very accurate closed-form expression for W (representing the energy barrier for particle detachment), thus extending previous results in the literature.