Some trace inequalities for discrete groups of Mobius transformations

We show that if (A, B) is discrete where A, B epsilon SL(2, C) and if tr(ABA(-1)B(-1)) not equal 2, tr(ABAB(-1)) not equal 2, and /tr(2)(A) - 4] less than or equal to 2(cos(2 pi/7) + cos(pi/7)- 1) = 1.0489..., then /tr(ABA(-1) B-1) - 2/ greater than or equal to 2 - 2 cos(pi/7) = 0.198.... It follows from above that if (X, Y) is discrete with tr(X) = tr(Y) not equal 0 and tr(XYX(-1) Y-1) not equal 2, then /tr(XYX(-1)Y(-1)) - 2/ greater than or equal to 2 - 2 cos(pi/7) = 0.198.... Both inequalities are sharp.