Weird Logarithms #2

If a, b are co-prime numbers satisfying the condition

${ \left( { 2 }+\sqrt { 3 } \right) }^{ \left( \frac { 1 }{ \log _{ a }{ \left( { 2 }-\sqrt { 3 } \right) } } +\frac { 1 }{ \log _{ b }{ \left( \frac { \sqrt { 3 } -{ 1 } }{ \sqrt { 3 } +{ 1 } } \right) } } \right) }=\frac { 1 }{ 12 }$ , then value of ab equal to ?