I managed to do it by planning ahead. I had two Industrial era music works completed and I faith-bought a third before I got to the Modern era. Faith-bought a Great Engineer (did I mention I was playing as the Byzantines ) and had Broadway done quickly. Probably a coincidence, but I struggled with Hermitage because, by that point, nobody had any art to trade. Also, Great Art can be sometimes difficult to get (all my museums end up filled with artifacts).