I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mistake I made. I apologize for how long this is. All assistance is appreciated.

Problem is

where

is in QIII

and

is in QII

sinA= so the hypotenuse is 5, the oppose side is -3, making the adacent side 4. Thus tan(A) = .

for B, cosB= so the hypotenuse is 4, the adjacent side -1, making the opposite side . Thus tan(b) = or just .

The tangent sum identity is

Substituting in, I get

which is

and then

followed by

and finally

unfortunately, the answer would appear to be

Can someone please point out my mistake?