[math-fun] Was: Re: Trivial soln for AX=XB in quaternions

Given points A,B on the unit circle in the complex plane, let theta=angle(A,0,B). Quickly give me a triple X,Y,Z such that theta/2=angle(X,Y,Z). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . theta/2=angle(A,1,B). Or Y=-1,i,-i. (Euclid's Inscribed Angle Theorem)