# Trying to calculate the value of pi^/490. Although I know the exact value (which I found on google to be pi^/490 but I wanted to derive it by myself.

Trying to calculate the value of $\frac{{\pi }^{4}}{90}$. Although I know the exact value (which I found on google to be $\frac{{\pi }^{4}}{90}$) but I wanted to derive it by myself. While doing so, I arrived at this rather peculiar expression: $C=\frac{7{ℼ}^{4}}{720}-\frac{1}{2}-\frac{P}{2}$
where $C$ is the value of the composite zeta function at $2$ and $P$ is the prime zeta function at $2$. My question is this. What will be the value of $C$?
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Assuming
$\zeta \left(s\right)=\sum _{n}\frac{1}{{n}^{s}}$

then
$\mathcal{C}\left(s\right)=\zeta \left(s\right)-P\left(s\right)-1$
and$\mathcal{C}\left(2\right)=\zeta \left(2\right)-P\left(2\right)-1=\frac{{\pi }^{2}}{6}-P\left(2\right)-1\approx 0.192687$