Ah, well if you already did it, I'll admit to the way I found it.

I started with the trajectory equation:

Plugging in a=b=0, y=2, x=15, g=9.81, rearranging the equation to "velocity equals", and using the trig. identity, tangent squared of the angle plus one = secant squared of the angle, I obtained:

From here, I used calculus to obtain the derivative of velocity with respect to angle:

The minimum velocity angle will occur when the above derivative equals 0. Equating the derivative to zero, using the reverse of the same trig identity as above and rearranging the equation will yield a quadratic equation:

Solving this equation yield two answers:

These are, of course, the numerical answers for the tangents of the angles. So, to find the angles, one must take the inverse tangent. Doing this for both answers will give you a possibility of four answers to choose from. Upon analysis, though, only one will make sense:

Arcane, why isn't there enough information? My only assumption was that the lowest velocity occurs where the derivative with respect to the angle equals zero. Also, the other three angles either point into the ground or in the opposite direction of the hole. The velocity ends up being 12.96 m/s for me. Why is the angle not correct?