Well hidden and threatening to disappear, Developer`TrigToRadicals seems able to do all trig pi/n. n = 34 gives a ridiculous mess that Corey's denester cracks, but into unmanageably large pieces. Some Macsymas know that Sin[Pi/34] ==((-Sqrt[Sqrt[17] + 3]*Sqrt[4*Sqrt[17] - 2*Sqrt[34 - 2*Sqrt[17]]] + Sqrt[34 - 2*Sqrt[17]] + Sqrt[17] - 1)/16) But I'm amazed at #==Apart[Simplify[Developer`TrigToRadicals[#]]]&@Sin[Pi/13/2] Sin[Pi/26] == (1/12)*(-1 + Sqrt[13]) + (1/12)*I*(I + Sqrt[3])* ((1/2)*(26 - 5*Sqrt[13] - 3*I*Sqrt[39]))^(1/3) + ((1 + I*Sqrt[3])*(-13 + Sqrt[13]))/ (12*2^(2/3)*(26 - 5*Sqrt[13] - 3*I*Sqrt[39])^(1/3)) . Also, the denester and I managed to bash 42 down to Sin[Pi/42] == ((2 + 6*I*Sqrt[3])^(1/3)* (3*I - 5*Sqrt[3] + Sqrt[7] - I*Sqrt[21]))/(24*2^(2/3)*7^(1/6)) - (1/6)*I*((1/2)*(-14*I + Sqrt[7] + 3*I*Sqrt[21]))^ (1/3) + (1/6)*I*((1/2)*(14*I + Sqrt[7] + 3*I*Sqrt[21]))^(1/3) + (1/12)*(1 + Sqrt[21]) which is better than I got with sin(pi/6 - pi/7). --rwg