Let the function $f: [0,1] \rightarrow \mathbb{R}$ be defined by
$$f(x) = \frac{4^{x}}{4^{x} + 2}$$
Then the value of
$$f\left(\frac{1}{40}\right) + f\left(\frac{2}{40}\right) + f\left(\frac{3}{40}\right) + \cdots + f\left(\frac{39}{40}\right) - f\left(\frac{1}{2}\right)$$
is $\_\_\_\_$