Functional differentiation of the Brueckner-theory equations gives a prescription for calculating the effective interaction in a Fermi liquid. The many terms that result from the differentiation are calculated for the liquid-${\mathrm{He}}^{3}$ system using \O{}stgaard's reaction matrices. ${\mathrm{He}}^{3}$ is strongly interacting in the sense that the defect wave-function probability $\ensuremath{\kappa}$ is large, of the order 0.56. As a result, many of the terms contribute substantially to the total. Of the Landau parameters ${f}_{0}$, ${f}_{1}$, and ${z}_{0}$, only ${z}_{0}$ is in reasonable agreement with experiment. The parameter ${f}_{0}$ is too small. This is known to be due in part to the neglect of three-body clusters. We find a small value for ${f}_{1}$, implying that the effective mass ${m}^{*}$ is close to one. Larger effective masses could be obtained by treating low-momentum-transfer processes more carefully and by summing higher-order diagrams.