trigonometry - Sides of a triangle are in Arithmetic Progression, then find $tan (alpha+ frac{beta}{2})$

The sides of a triangle are in Arithmetic Progression. If the smallest angle of the triangle is $\alpha$ and largest angle of the triangle exceeds the smallest angle by $\beta$, then find the value of $\tan (\alpha+ \frac{\beta}{2})$

Would it be correct to assume sides of triangle of as $1,2,3$ and then apply cosine rule to find angles? Or could someone propose a better approach?