Answer by user90369 for Do the roots of this equation involving two Euler products all reside on the critical line?

The equation doesn’t hold, because:$$\lim\limits_{s\downarrow 0} s\zeta(s+1)=1\ne\frac{\pi}{3}=\lim\limits_{s\downarrow 0} \frac{\zeta(2-s)2^s\pi^{s-1}\cos(\frac{\pi s}{2})\Gamma(3-s)}{s(s+1)}$$and$$\lim\limits_{s\uparrow 1} \frac{1}{(1-s)\zeta(2-s)}=1\ne\frac{3}{\pi}=\lim\limits_{s\uparrow 1} \frac{2^s\pi^{s-1}\Gamma(3-s)}{\zeta(s+1)s(s+1)}\frac{\cos(\frac{\pi s}{2})}{1-s}$$