JEE Advanced 2023 Mathematics question on Trigonometry

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

Let $a$ be the area of the triangle $ABC$. Then the value of $\left(64a\right)^2$ is