Trigonometry

tan(9pi/8)=\(\sqrt{2}-1\) or \(\approx 0.41421356\)

tan (x / 2)  =  csc x - cot x

So...

tan (9pi/8) =

csc (9pi/4) - cot (pi/4)  = 

csc (pi/ 4)   - cot (pi/ 4) =

sqrt (2) - 1

As tertre found   .....!!!