The first equation of the set

Algebra Level 2

Let \(x,y,z\) be the real numbers such that \(xyz=1\). Find the value of

\[F=\dfrac { 1 }{ 1+x+xy } +\dfrac { 1 }{ 1+y+yz } +\dfrac { 1 }{ 1+z+zx } . \]

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