A trigonometric problem

Geometry Level 4

If \(\tan A\) and \(\tan B\) are the roots of \(x^2 - 12x + 32 = 0\).

What is the value of

\[ \sin^2(A+B)- 12\sin(A+B)\cos(A+B) + 32\cos^2(A+B) ? \]

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