Dirty Algebra

Geometry Level 3

a1a2=16{ a }\sqrt { 1-{ a }^{ 2 } } =\frac { 1 }{ \sqrt { 6 } }

Given that the equation above is fulfilled for 0<a<10<a<1, find a6+(1a2)3{ a }^{ 6 }+{ \left( 1-{ a }^{ 2 } \right) }^{ 3 }.

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