If A + B + C = 180°, then tanA + tanB + tanC equals:

Since A + B = 180° − C, we get tan(A + B) = −tanC, that is (tanA + tanB)/(1 − tanA·tanB) = −tanC. Cross-multiplying: tanA + tanB = −tanC + tanA·tanB·tanC, which rearranges to tanA + tanB + tanC = tanA·tanB·tanC. Check with A = B = C = 60°: both sides equal 3√3 ≈ 5.196.