Measuring B -> tau nu and B_c -> tau nu at the Z peak

The measurement of B->tau nu at the B factories provides important constraints on the parameter tan beta/m_H^+- in the context of models with two Higgs doublets. Limits on this decay from e+e- collisions at the Z peak were sensitive to the sum of B->tau nu and B_c->tau nu. Due to the possibly sizeable contribution from B_c->tau nu we suggest that a signal for this combination might be observed if the LEP L3 Collaboration used their total data of ~3.6 10^6 hadronic decays of the Z boson. Moreover, we point out that a future Linear Collider operating at the Z peak (Giga Z option) could constrain tan beta/m_H^+- from the sum of these processes with a precision comparable to that anticipated at proposed high luminosity B factories from B-> tau nu alone.