Let the domains of the functions \( f(x)=\log_{4}\log_{3}\log_{7}\left(8-\log_{2}\left(x^{2}+4x+5\right)\right) \) and \( g(x)=\sin^{-1}\!\left(\dfrac{7x+10}{x-2}\right) \) be \( (\alpha,\beta) \) and \( [\gamma,\delta] \), respectively. Then \( \alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2} \) is equal to:
