(i) Use the substitution \(u = \tan x\) to show that, for \(n \neq -1\),

\(\int_0^{\frac{\pi}{4}} (\tan^{n+2} x + \tan^n x) \, dx = \frac{1}{n+1}.\)

(ii) Hence find the exact value of

(a) \(\int_0^{\frac{\pi}{4}} (\sec^4 x - \sec^2 x) \, dx,\)

(b) \(\int_0^{\frac{\pi}{4}} (\tan^9 x + 5 \tan^7 x + 5 \tan^5 x + \tan^3 x) \, dx.\)