If A + B = 60° and tanA + tanB = 3, then tanA·tanB equals:

tan(A + B) = (tanA + tanB)/(1 − tanA·tanB), so √3 = 3/(1 − p) where p = tanA·tanB. Then 1 − p = 3/√3 = √3, giving p = 1 − √3 ≈ −0.732. The negative product is legitimate: the two tangents here are about 3.227 and −0.227, i.e. A ≈ 72.8° and B ≈ −12.8°, which do add to 60°.