A fatty acid beta-oxidation pathway by which fatty acids having cis-double bonds on odd-numbered carbons are degraded. In this pathway, a cis-3-enoyl-CoA is generated by the core beta-oxidation pathway, and then converted to a trans-2-enoyl-CoA, which can return to the core beta-oxidation pathway for complete degradation. Fatty acid beta-oxidation begins with the addition of coenzyme A to a fatty acid, and ends when only two or three carbons remain (as acetyl-CoA or propionyl-CoA respectively).