Given that \(\dfrac{d}{dx}(\tan x)=\sec^2 x,\) differentiate \(\tan^3x\) with respect to \(x\).

Show that \[ \tan^4x=\tan^2x \sec^2x- \sec^2x+1 \] and hence evaluate \[ \int_0^{\pi/4}\tan^4x \, dx. \]

Given that \(\dfrac{d}{dx}(\tan x)=\sec^2 x,\) differentiate \(\tan^3x\) with respect to \(x\).

Show that \[ \tan^4x=\tan^2x \sec^2x- \sec^2x+1 \] and hence evaluate \[ \int_0^{\pi/4}\tan^4x \, dx. \]