Special values of generalized log-sine integrals

We study generalized log-sine integrals at special values. At π and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at ±1. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at π/3 which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided.