How

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 $b^2-B^2$ .