I have been struggling for a while on evaluating this definite infinite product integral:
$$\int_{-\frac{\pi}{4}}^0(1+\tan{x})(1+\tan^2x)(1+\tan^4x)(1+\tan^8x)(1+\tan^{16}x)...dx$$
This is a question given by my maths teacher a while back and I have been struggling with it ever since. I have tried so many different substitutions and I have even tried integrating by parts (do NOT do this), but nothing has led me even close to an answer. I'm guessing there is trig identity I must be missing in order to simplify the inside of the integral? or some wonder substitution?
Any help would be greatly appreciated.