Cyg X-3 is a high-mass X-ray binary, and is the only system in the Milky Way consisting of a Wolf-Rayet star and a compact object. The nature of the compact object (neutron star / black hole) is still unclear. Despite numerous studies, Cyg X-3 remains a unique and puzzling system. In our study, we present a detailed physical modeling of Cyg X-3 gamma-ray data, allowing us to drastically improve our understanding of this complex system. We perform fitting of the gamma-ray spectrum and light curve with our complex physical model and firmly establish that the jet of the compact object has to be inclined with respect to the orbital axis. Additionally, we test for the first time the predictions of General Relativity (GR) for the precession of the inclined jet in the system and find the predictions for the black hole compact object hypothesis in disagreement with the 50-year-long sample of observational data in the radio band. Finally, we incorporate in our data set available infrared (IR) measurements that constrain the synchrotron emission from the jet and its modulation, and test a physical scenario where the jet is bent and is precessing due to the influence of the stellar wind, as well as is bent by the Coriolis force.