7 doesn't seem nice?

Geometry Level 5

The angles of \(\Delta ABC\) are in the ratio \(1:2:4\). \(\Delta ABC\) is inscribed in a circle of unit radius. The area of \( \Delta ABC \) is of the form \( \frac { \sqrt{a} } {b} \), where \(a\) and \(b\) are coprime integers. What is the value of \( a^2 + b^2 \)?

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