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Accurate prediction of experimental results is one of the main goals in scientific research. With higher complexity this relies increasingly on accurate numerical simulations. The inductive detection of magnetic nanoparticles often relies on the nonlinear magnetization response of these particles on externally applied time-varying magnetic fields. However, in some cases a closed analytical solution for special cases can be found and used for calibration as well as testing numerical codes. Furthermore, they allow the systematic study of the system and can be starting points for perturbation theory. In this work an analytical solution for the simplest RDS-experiment for magnetic nanoparticles in solution with full 3D motion is presented and compared to the known case of 2D-confined rotation of the nanoparticles.