A trigonometric problem

Geometry Level 4

If tanA\tan A and tanB\tan B are the roots of x212x+32=0x^2 - 12x + 32 = 0.

What is the value of

sin2(A+B)12sin(A+B)cos(A+B)+32cos2(A+B)? \sin^2(A+B)- 12\sin(A+B)\cos(A+B) + 32\cos^2(A+B) ?

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