The area of the region bounded by the curve $y = \tan x$, the $x$-axis and the tangent to the curve $y = \tan x$ at $x = \frac{\pi}{4}$ is\\
(A) $\log_e 2 - \frac{1}{2}$\\
(B) $\log_e 2 + \frac{1}{2}$\\
(C) $\frac{1}{2}\left(\log_e 2 - \frac{1}{2}\right)$\\
(D) $\frac{1}{2}\left(\log_e 2 + \frac{1}{2}\right)$.