This situation is really not that deep. I'm not a Sigma so therefore I will not speak for them but as Zetas, no, we do not have a connection to Sigma Lambda Beta or Sigma Lambda Gamma for that matter. But, in some areas there is a close family like atmosphere that is beneficial to all parties in terms of support for events and programs. Where I'm from we don't have Betas or Gammas so we don't refer to them as our "cousins" but I'm not going to outright down others who may feel that connection. It doesn't take anything away from our beautiful foundation or the special and unique bond we have with Phi Beta Sigma.
Anyway, Soror we are trying to get to know everyone on this side of GC so could post your info in the new introductory thread that we started?