Let $$ D=\{z \in \mathbb{C} : 0<\Re(z)<\frac{1}{2} \text{ or } \frac{1}{2}<\Re(z)<1 \} $$ that is the critical strip without critical line.

I have to find if the following equation, with Gamma Euler function, has any root in $D$ $$ \Gamma(z) = \dfrac {\pi^z} {\cos \left( \dfrac{\pi}{2} \cdot z \right) \cdot 2^{1-z} } \cdot \dfrac {1-2^{1-z}} {1-2^z} $$

Thanks.