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Algebra Level pending

Given: \(sin(x)\, +\, cos(x)\, =\, \frac { 1 }{ 2 }\) And \({ sin }^{ 3 }(x)\, +\, { cos }^{ 3 }(x)\, =\, \frac { a }{ b } \)

Find: \(b\, -\, a\) such that \(a\) and \(b\) are co-prime integers.

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