Terpene cyclase that catalyzes the cyclization of farnesyl diphosphate (FPP) to various sesquiterpenes, including beta-copaene, alpha-cubebene, cadina-1(6),4-diene, gamma-muurolene, delta-cadinene, epizonarene, epicubenol and cubenol (PubMed:32233445). Agr4 is also able to use the monoterpene precursor geranyl diphosphate (GPP) as substrates to synthesize the monoterpene beta-myrcene (PubMed:32233445). Delta-cadinene is the major product of Agr4 (PubMed:32233445). (2E,6E)-farnesyl diphosphate = delta-cadinene + diphosphate (2E,6E)-farnesyl diphosphate = diphosphate + gamma-muurolene (2E,6E)-farnesyl diphosphate = beta-copaene + diphosphate (2E)-geranyl diphosphate = beta-myrcene + diphosphate The DDXXD motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.