Albert Rich points out that you get simplification when the complex cube root denests in 2 1/6 1/3 atan(x) (x + 1) (%i - x) sin(-------) = ------------- + ------------- . 3 1/3 2 1/6 2 (%i - x) 2 (x + 1) This seems to happen fairly rarely, but a nice one is 1/3 4 + 1 atan(--------) 1/3 sqrt(3) 4 - 1 tan(--------------) = --------, 3 sqrt(3) easily checked by cubing, but not so easily found. Still no luck with sqrt(binomial) = hexanomial.