In a triangle ABC, tanA + tanB = 4 and tanA·tanB = 3. The value of tanC is:

In any triangle tanA + tanB + tanC = tanA·tanB·tanC, so 4 + tanC = 3tanC, giving 2tanC = 4 and tanC = 2. Concretely tanA and tanB are the roots of $x^2-4x+3=0$, namely 1 and 3, so $A=45$°, B ≈ 71.57° and C ≈ 63.43°, whose tangent is indeed 2.