= Solution
Keep the color matrix intact: $\mathcal A_\mu=A^a_\mu T^a$. Under <parity>, invariance of its contraction with the <vector current> requires
$$
\boxed{\mathcal A_\mu(x)\stackrel P\longmapsto\Lambda_\mu{}^\nu\mathcal A_\nu(x_P).}
$$
Under <charge conjugation>, the fermionic reordering in part (b) transposes the color matrix as well as the spinor matrix. For a fixed color matrix $M$, $\bar\psi M\gamma^\mu\psi$ becomes $-\bar\psi M^T\gamma^\mu\psi$. Hence invariance of the interaction requires
$$
\boxed{\mathcal A_\mu(x)\stackrel C\longmapsto-\mathcal A_\mu(x)^T.}
$$
This is not a rule that changes the sign of every individual color component: transposition also acts on the generators of the <fundamental representation>.
Write the <gauge field strength> as $\mathcal F_{\mu\nu}=\partial_\mu\mathcal A_\nu-\partial_\nu\mathcal A_\mu+ig[\mathcal A_\mu,\mathcal A_\nu]$. Since $[A^T,B^T]=-[A,B]^T$, the <charge conjugation> rule gives $\mathcal F_{\mu\nu}\mapsto-\mathcal F_{\mu\nu}^T$. Including the coordinate reflection in <CP symmetry>,
$$
\boxed{\mathcal F_{\mu\nu}(x)\stackrel{CP}\longmapsto
-\Lambda_\mu{}^\alpha\Lambda_\nu{}^\beta\mathcal F_{\alpha\beta}(x_P)^T.}
$$
For generators normalized by $\operatorname{Tr}(T^aT^b)=\kappa\delta^{ab}$, the color contraction equals $\kappa^{-1}\operatorname{Tr}(\mathcal F_{\mu\nu}\mathcal F_{\rho\sigma})$. The two charge-conjugation minus signs cancel, and transposition reverses the order inside the trace without changing it. The <Levi-Civita symbol> acquires $\det\Lambda=-1$ under the remaining reflection. Thus
$$
\boxed{\mathcal L_\theta(x)\stackrel{CP}\longmapsto-\mathcal L_\theta(x_P).}
$$
\b[The <Yang-Mills theta term> is CP-odd; a generic fixed nonzero $\theta$ produces <CP violation>.] Setting $\theta=0$ removes this source. Although the density is a total derivative, it can affect the quantum theory through nontrivial topological sectors; the local transformation test is not rendered irrelevant by that fact.
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