In a very recent article (M.G. Marmorino, J. Math. Chem. 32 (2002) 303), exact ground and first-excited state eigensolutions determined by trial and error have been introduced for the one-dimensional Hamiltonian with a constant multiple of a squared cotangent potential nu(nu-1) cot(2) x on the domain x is an element of(0, pi). An explicit formula for the full spectrum was then proposed by the help of numerical experiments. In the present study, the results of Marmorino are mathematically justified and generalized by transforming the problem into an equivalent hypergeometric form.