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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