The area between two curves $f(x)$ and $g(x)$ from $a$ to $b$ is given by $\int_a^b |f(x) - g(x)| dx$. In this case, $f(x) = \sec x$ and $g(x) = \tan x$, and we are integrating from $0$ to $\pi/2$. So, we have:
$$\int_0^{\pi/2} |\sec x - \tan x| dx =
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