Couple of hints.

1) As mentioned in the problem, the identity from 4.10 will be helpful here. Remember that all that matters in terms of the variables is the relative positions of the sides and angles. Hence the identity in 4.10 could be written as$$\frac{b-c}{b+c} = \tan((B-C)/2) \tan(A/2).$$

2) As long as the ratio $b/c$ is the same, the actual side lengths of the triangle do not matter. Thus, we can assume for convenience that $b = 2 + \sqrt{3}$ and $c = 1$.