Flip flops

Algebra Level pending

Suppose that \(a, b\), and \(c\) are real numbers greater than one. Find the value of \[ \large \frac { 1 }{ 1+\log _{ { a }^{ 2 }b }{ \frac { c }{ a } } } +\frac { 1 }{ 1+\log _{ { b }^{ 2 }c }{ \frac { a }{ b } } } +\frac { 1 }{ 1+\log _{ { c }^{ 2 }a }{ \frac { b }{ c } } } \]

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