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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