= Solution
For $SU(3)_L^3$, the three right-flavour copies of $\chi$ contribute $3$, while $\eta$ contributes $-1$, giving $2$. For $SU(3)_L^2U(1)_X$, these fields contribute $3(-1/2)+(-1/2)=-2$. All fifteen components of $\chi$, $\eta$, and $\widetilde\eta$ have charge $-1/2$, so
$$
\mathcal A[U(1)_X^3]=15\left(-\frac12\right)^3=-\frac{15}{8},
\qquad
\mathcal A[U(1)_X\text{-gravity}]=15\left(-\frac12\right)=-\frac{15}{2}.
$$
The ultraviolet formulas at $N_f=3$ give $2$, $-2$, $-15/8$, and $-15/2$ respectively. Every <'t Hooft anomaly> therefore matches.
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