Tangent Tango 2

Geometry Level 4

If tan212°\tan^2 12°, tan224°\tan^2 24°, tan248°\tan^2 48°, and tan296°\tan^2 96° are the roots of the polynomial f(x)=x4+Ax3+Bx2+Cx+Df(x) = x^4 + Ax^3 + Bx^2 + Cx + D, find A+2B+3C+4DA + 2B + 3C + 4D.

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