Triplet excitation energies are calculated from the response eigenvalue equation for the coupled cluster singles and doubles (CCSD) model using an integral direct approach and an explicit spin coupled triplet excitation space. The cost of one linear transformation for the triplet excitation energy is about two times the cost of one linear transformation for the singlet excitation energy. The triplet excitation spectrum of benzene is calculated using from 147 to 432 basis functions. The calculated triplet excitation energies are compared with experimental and other theoretical values.