I have the equation f(x) = $\displaystyle ln \tan(\frac{\pi}{4} + x)$ and I want to show that the derivative f ' (x) is equal to $\displaystyle 2\sec 2x$.

I have gotten an expression for the derivative as $\displaystyle \csc(\frac{\pi}{4} + x) \sec(\frac{\pi}{4} + x)$ but I'm not sure what I can do in order to show this is equal to 2sec2x.

Please could you help me get closer to the answer? Thanks if you know what can be done with this :)