Check Your Natural Talent(4)!

Using the property, $\Gamma (s) \zeta (s) = \displaystyle \int_0^\infty \dfrac {x^{s-1}}{e^x - 1} dx$

Where $\Gamma (•)$ and $\zeta (•)$ denote Gamma Function and Reimann Zeta Function respectively.

Put $s= 4,$ $\Gamma (4) \zeta (4) = \displaystyle \int_0^\infty \dfrac {x^{4-1}}{e^x - 1} dx = S$

$\Gamma (s) = (s-1)!$ where $(!)$ denote factorial and $\zeta (s) = \displaystyle \sum_{k=1}^\infty \dfrac {1}{k^s}$

$S = {\color{#20A900}{\Gamma (4)}}{\color{#D61F06}{ \zeta (4)}} = {\color{#20A900}{(4-1)!}} \times {\color{#D61F06}{\dfrac {π^4}{90} }} = \dfrac {(1)π^4}{15} = \dfrac {aπ^b}{c}$

Therefore, $2(a +c) + b = 2( 1 + 15) + 4 = \boxed{36}$