Let the domains of the functions $f(x)=\log_7\left(\log_7\left(\log_7\left(8-\log_2(x^2+4x+5)\right)\right)\right)$ and $g(x)=\sin^{-1}(2x-3)$ be $(\alpha,\beta)$ and $[\gamma,\delta]$, respectively. Then $\alpha^2+\beta^2+\gamma^2+\delta^2$ is equal to: