Let $$f(x) = 7 \tan^8 x + 7 \tan^6 x - 3 \tan^4 x - 3 \tan^2 x$$ for all $$x \in \left(-\frac{\pi}{2}, \frac{\pi}{2} \right).$$ Then the correct expression(s) is(are)

A

$$\int_{0}^{\frac{\pi}{4}}xf(x)dx = \frac{1}{12}$$

B

$$\int_{0}^{\frac{\pi}{4}}f(x)dx = 0$$

C

$$\int_{0}^{\frac{\pi}{4}}xf(x)dx = \frac{1}{6}$$

D

$$\int_{0}^{\frac{\pi}{4}}f(x)dx = 1$$