Could someone double-check this for me please?

Find the exact value by using a half-angle identity.

tan(7pi/8)

My Answer: tan(7pi/8) can be turned into tan(7pi/4 /2). So then we use the half angle formula associated with tan: tan A/2=sin A/(1 cosA)

That gives us tan(7pi/4 /2)=(sin 7pi/4)/(1 cos 7pi/4)

=-sqrt2/2/(1 sqrt2/2)

=-sqrt2(2 sqrt2)

=-sqrt2(2-sqrt2)/2

=(2-2sqrt2)/2

=1-sqrt2