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In recent studies, several active galactic nuclei (AGNs) have exhibited gradients of the Faraday rotation measure (RM) transverse to their parsec-scale jet direction. Faraday rotation likely occurs as a result of a magnetized sheath wrapped around the jet. In the case of 3C 273, using Very Long Baseline Array multiepoch observations at 5, 8, and 15 GHz in 2009–2010, we observe that the jet RM has changed significantly toward negative values compared with that previously observed. These changes could be explained by a swing of the parsec-scale jet direction, which causes synchrotron emission to pass through different portions of the Faraday screen. We develop a model for the jet–sheath system in 3C 273 where the sheath is wider than the single-epoch narrow relativistic jet. We present our oversized sheath model together with a derived wide-jet full intrinsic opening angle αint = 2.°1 and magnetic field strength B∣∣ = 3 μG, and thermal particle density Ne = 125 cm−3 at the wide jet–sheath boundary 230 pc downstream (deprojected) from its beginning. Most of the Faraday rotation occurs within the innermost layers of the sheath. The model brings together the jet direction swing and long-term RM evolution and may be applicable to other AGN jets that exhibit changes in their apparent jet direction. [ABSTRACT FROM AUTHOR]