Entry $(2,2)$ of $C$ equals $R_0(r) - i\,\Theta_0(\theta)$

Fourth coefficient check of the separation $C^{(\varsigma)} = R^{(\varsigma)}(r) + i\Theta^{(\varsigma)}(\theta)$ (Hintz, text after eq. (7)): at every point of $U$ the $(2,2)$ entry of $C^{(\varsigma)} = (\det X)X^{-1}(c^{(\varsigma)}I - B^{(\varsigma)})(X^*)^{-1}$ equals $R_0^{(\varsigma)}(r) + i\,(-\Theta_0^{(\varsigma)}(\theta))$, with $R_0$ and $\Theta_0$ the explicit paper coefficients (the $(2,2)$ entry of $\Theta$ is $-\Theta_0$). Proved by the same denominator-clearing polynomial verification.