Last week I had the pleasure to meet Albert Rich (of Derive fame), who introduced me to a class of simplifications including sqrt(15) 2 atan(--------) 9 sqrt(15) - sqrt(3) sin(----------------) = ------------------ . 3 8 With Macsyma I then concocted 1/3 9 - 3 4 atan(----------) 1/2 4/3 4/3 1/3 4/3 5 3 (4 + 2 - 7) - 6 4 - 2 + 10 tan(----------------) = ------------------------------------------- 3 5 It isn't even trivial to *verify* this symbolically. Along the way we exposed a bug in my MULTIPLY_CONJUGATES function wherein the imaginary unit, replaced by an explicit sqrt(-1), prematurely reverted to the symbol %I. --rwg