Please answer the following two questions. ?

tan A + tan B
    = (tan^2 A - tan^2 B)/(tan A - tan B)
    = (sec^2 A - 1 - sec^2 B + 1)/(tan A - tan B)
    = (sec^2 A  - sec^2 B)/(tan A - tan B)


4/15 = tan(x)/(1+cot(x))
        = tan(x)/(1+1/tan(x))
         = tan^2(x)/(1+tan(x))
∴ tan^2(x) - (4/15)tan(x) - 4/15 = 0
∵ π < x < 3π/2
∴ tan(x) > 0
∴ tan(x) = [4/15 + √(16/225+16/15)]/2
              = (4/15 + 16/15)/2
              = 2/3