\Phi=-\theta lnZ=-\theta ln\Pi_kZ_k=-\theta\sum_klnZ_k=-\theta\sum_kln(1\mp e^{-\frac{\epsilon_k-\mu}{\theta}})}^{\mp1}=\pm \theta\sum_kln(1\mp e^{-\frac{\epsilon_k-\mu}{\theta}})