trigonometry - Trigonometric AP relation on sides of a triangle

The sides of a triangle are in AP (Arithmetic Progression) and the greatest angle exceeds the least angle by $90$ degrees prove that the sides are proportional to $7^{\frac{1}{2}}+1$ , $7^{\frac{1}{2}}$ and $7^{\frac{1}{2}}-1$.

I tried to use the following property "when the sides of a triangle are in AP then the $\cot$ of half the angles are also in AP" but I couldn't get anything please help.