Mathematics

Problem

x, y, z

satisfy the condition that any two of them are equal, evaluate the determinant:

\begin{vmatrix} 1 & 1 + \tan x & \tan x + \tan^2 x \\ 1 & 1 + \tan y & \tan y + \tan^2 y \\ 1 & 1 + \tan z & \tan z + \tan^2 z \end{vmatrix}

(A)

\tan(x + y + z)