Prepare a Bloch state with R_Y and R_Z

Starting from $\lvert0\rangle$, prepare the state with Bloch angles $\theta=\tfrac{2\pi}3$ and $\phi=\tfrac\pi4$, that is $\lvert\psi\rangle=\cos\tfrac\pi3\lvert0\rangle+e^{i\pi/4}\sin\tfrac\pi3\lvert1\rangle=\tfrac12\lvert0\rangle+\tfrac{\sqrt3}2e^{i\pi/4}\lvert1\rangle$, using only the gates $R_Y(\theta)=\begin{pmatrix}\cos\frac\theta2&-\sin\frac\theta2\\\sin\frac\theta2&\cos\frac\theta2\end{pmatrix}$ and $R_Z(\phi)=\mathrm{diag}(e^{-i\phi/2},e^{i\phi/2})$, at most two gates in total. A global phase is allowed: the check measures the fidelity $\lvert\langle\psi\vert\chi\rangle\rvert^2$.