Properties Of Triangle

Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

\(\text { Let } a \text { be the area of the triangle } A B C \text {. Then the value of }(64 a)^2 \text { is }\) :