Derivation $($up to $8$ pts extra credit!$)$

Derive an expression for the entropy of a pure atomic crystal of $N$ nuclei, given its partition proposed by Einstein is given by: $Q=e^{-U_0}(\frac{e^{-h\frac{v}{2}}}{1-e^{-hv}}{)}^{3N},$ where $U_0$ is the sublimation energy at $0K.$ Recall that $S=k_{B}T(\frac{dlnQ}{dT}{)}_{N,V}+k_{B}lnQ.$