\[\lim _{ n\rightarrow \infty }{ \frac { 2{ F }_{ n+8 } }{ { F }_{ n } } } ={ F }_{ \alpha }\sqrt { { F }_{ \beta } } +{ F }_{ \gamma }-F_{ \delta }\]
Let \(F_n\) denote the \(n^\text{th} \) Fibonacci number. Find \(\alpha +\beta +\gamma +\delta\).

#### This problem is original.

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