A couple of years ago I restated an almost forgotten identity equivalent to %pi %pi 6 theta (---, q) = theta (---, q) = sqrt(3) eta(q ) 2 6 1 3 3 2 6 theta (0, q ) theta (0, q ) 2 4 1/3 = sqrt(3) (---------------------------) , 2 in this form as special values of Theta(pi/n) in terms of eta or equivalently the "theta constants" theta[s](0,q^k). What is the analogous value with the lhs 1 and 2 switched? 2 2 12 %pi %pi eta (q ) eta(q ) theta (---, q) = theta (---, q) = ----------------- 2 3 1 6 4 6 eta(q ) eta(q ) 3 9 theta (0, q ) theta (0, q) - 3 theta (0, q ) 2 2 1/3 2 2 = theta (0, q ) (---------------) = ------------------------------. 4 6 2 2 theta (0, q ) 4 This is a rich area of nonobvious(?) identities, e.g., 2 6 6 theta (0, q) theta (0, q ) theta (0, q ) 2 2 3 2 2 2 3 = theta (0, q ) theta (0, q ) theta (0, q ), 2 3 2 or equivalently 2 6 theta (0, q) theta (0, q) theta (0, q ) 3 4 4 2 2 3 3 = theta (0, q ) theta (0, q ) theta (0, q ) 4 3 4 --rwg