To simplify the expression (1 - tan^2(pi/8)) / (1 + tan^2(pi/8), we can use the trigonometric identity:

tan^2(x) = sec^2(x) - 1

Using this identity, we can rewrite the expression as:

(1 - (sec^2(pi/8) - 1)) / (1 + (sec^2(pi/8) - 1))

Simplifying further, we get:

((-sec^2(pi/8) + 2) / (sec^2(pi/8))

Therefore, the simplified expression is (-sec^2(pi/8) + 2) / sec^2(pi/8).