In this article, we have developed and evaluated a method for obtaining extreme ultraviolet (EUV) radiation by amplifying the third harmonic of the free-electron laser (FEL) radiation using phase shifters and tapering. Simulations of self-amplified spontaneous emission (SASE) FELs and seeding schemes are presented. We have demonstrated that the combination of phase shifts and tapering results in a more efficient technique that reduces electron beam energy by half. The stability of the scheme in relation to phase shift errors has been analyzed, and the implementation of the method has been discussed. The proposed FEL design enables a decrease in facility energy and a reduction in the cost of both new and existing projects in the EUV band.