Is it possible to show that: \begin{align} \frac{\Gamma\left(\frac{1}{78}\right) \Gamma\left(\frac{29}{78}\right) \Gamma\left(\frac{35}{78}\right) \Gamma\left(\frac{53}{78}\right) \Gamma\left(\frac{55}{78}\right) \Gamma\left(\frac{61}{78}\right)}{\Gamma\left(\frac{2}{78}\right) \Gamma\left(\frac{28}{78}\right) \Gamma\left(\frac{32}{78}\right) \Gamma\left(\frac{44}{78}\right) \Gamma\left(\frac{58}{78}\right) \Gamma\left(\frac{70}{78}\right) } = \sqrt{3} \end{align}
There are other known ratios of Gamma functions, but as always there seems to be a product rule or trick to evaluate the ratios.