Hit three expectation values

Starting from $\lvert0\rangle$, use at most three gates from $\{R_X, R_Y, R_Z, H, S, X, Z\}$ to prepare a state with

$\langle Z\rangle=\tfrac12,\qquad \langle X\rangle=\tfrac{\sqrt3}{2},\qquad \langle Y\rangle=0 .$

Each expectation value is graded with absolute tolerance $10^{-6}$. Recall that for $\lvert\psi\rangle=\cos\tfrac\theta2\lvert0\rangle+e^{i\phi}\sin\tfrac\theta2\lvert1\rangle$ the Born rule gives $\langle A\rangle=\langle\psi\vert A\vert\psi\rangle=\sum_m m\,P(m)$, which evaluates to $\langle X\rangle=\sin\theta\cos\phi$, $\langle Y\rangle=\sin\theta\sin\phi$, $\langle Z\rangle=\cos\theta$.