Find the exact value by using a half-angle identity. tangent of seven pi divided by eight.

tan (7pi/8) = -4.4142

Explanation:
The tangent half-angle formula is shown in the attached image
We have:
alpha = 7pi / 8
alpha/2 = 7pi / 16

Substitute in the formula with the alpha and alpha/2 as follows:
tan (7pi/8) = [2tan(7pi / 16)] / [1 - tan(7pi / 16)tan(7pi / 16)]
tan (7pi/8) = -4.4142

Hope this helps :)