Random Angle II

A right triangle is being formed with legs labeled $A$ and $B$. The random lengths of legs $A$ and $B$ are both IID Unif$(0,1)$ RVs. Let $\theta$ be the angle (of random degree measure) that is opposite of side $A$. Find the probability $\theta > \dfrac{\pi}{3}$. The answer is in the form $\dfrac{a}{b\sqrt{c}}$ for integers $a,b,c$ that are relatively prime. Find $abc$.