Let $$f(x) = \frac{1 - \tan x}{4x - \pi}, x \neq \frac{\pi}{4}, x \in \left[0, \frac{\pi}{2}\right]$$. If $$f(x)$$ is continuous in $$\left[0, \frac{\pi}{2}\right]$$, then $$f\left(\frac{\pi}{4}\right)$$ is

A

$$1$$

B

$$\frac{1}{2}$$

C

$$-\frac{1}{2}$$

D

$$-1$$