Trigonometry! #32

Geometry Level 4

If \(A\) and \(B\) are two angles satisfying \(0<A,B<\frac {\pi}{2}\) and \(A+B=\frac {\pi}{3}\), then find the minimum value of \(\sec A + \sec B\).

If your answer is simplified to \(\frac {a}{b}\), where \(a\) and \(b\) have no terms in common (other than one, maybe), enter the value of \(a^{2} + b^{2}\).

This problem is part of the set Trigonometry.

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