Race to end Fibonacci

\[\large{S=\left( { F }_{ 2015 }+{ F }_{ 2013 } \right) \left( { F }_{ 2013 }+{ F }_{ 2012 } \right) }\]

If \(F_{n}\) is the \(n^\text{th}\) Fibonacci term, and \(S\) can be expressed as \(F_{a}\), then find the value of \(\dfrac{a+2}{10}\)

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