Q3 is just a diode so gm3 can't play a role.
What is r23? What is VA? You need to define some of these parameters. I assume gm = β but am not sure ...
I analyzed the circuit assuming β → ∞. Why? Because any circuit that is β-dependent is not a good circuit.
So I got what looks like your expression if gm → ∞. I know that's not what you are trying to find out - sorry.