${\mathsf{R}\mathsf{T}}_2^2$ does not imply ${\mathsf{W}\mathsf{K}\mathsf{L}}_0$

We prove that ${\mathsf{R}\mathsf{C}\mathsf{A}}_0+{\mathsf{R}\mathsf{T}}_2^2\to ̸{\mathsf{W}\mathsf{K}\mathsf{L}}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not of PA-degree.