Method for producing aminothiazole derivative and production intermediate

A compound represented by formula (3): (wherein ring A represents a benzene ring or a 6-membered aromatic heterocycle; R 1 represents a hydrogen atom, a C 1-6 alkyl group, a halogen atom, a nitro group, an amino group, a mono-C 1-6 alkylamino group, or a di-C 1-6 alkylamino group; at least one of R 2 , R 3 , and R 4 represents a methoxy group, and the rest each represents a hydrogen atom, a C 1-6 alkyl group, a halogen atom, a nitro group, an amino group, a mono-C 1-6 alkylamino group, or a di-C 1-6 alkylamino group; and R 5 represents a hydrogen atom or an electron-withdrawing group selected from a halogen atom, a nitro group, a trifluoromethyl group, a trichloromethyl group, a cyano group, an acetyl group, a sulfonic acid group, and an alkylsulfonic acid group).