How

Algebra Level 3

If \( \beta + \cos^2 \alpha , \beta + \sin^2\alpha \) are the roots of the equation \(x^2+2bx+c=0 \) and \(\gamma + \cos^4 \alpha , \gamma + \sin^4 \alpha \) are the roots of the equation \(x^2 + 2Bx + C = 0 \), then find \(b^2-B^2\).

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