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Catalysis of the reaction: 3-O-[N-acetyl-alpha-D-galactosaminyl]-L-threonyl-[protein] + UDP-N-acetyl-alpha-D-glucosamine = 3-O-[N-acetyl-beta-D-glucosaminyl-(1->3)-N-acetyl-alpha-D-galactosaminyl]-L-threonyl-[protein] + H(+) + UDP.