# I Have Seen Sine, Cosine, What About Tangent?

Geometry Level 5

Suppose $$a, b, c$$ are sides of a triangle $$\Delta ABC$$ and the roots of the following equation. $x^3-24x^2+180x-420=0.$ If $$\tan A+\tan B+\tan C=-\dfrac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find the value of $$p+q$$.

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