I don't think so, at least there isn't anything in the statement that makes me think that way.
I came to the same conclusion, a·2/√3 gives the exact solution, I just can't find in the theory were it's justified why it is calculated this way. A mistake in the solution could be posible aswell, so...
Since in Debye aproximation Debye's frecuency is defined as the maximum frecueny , the corresponding wavelenght should be the minimum one, due to the inverse relation among those
λ=v/f=v·2π/ω=5.9 Å , which is higher than the given result.
I believe I should be using the information 'cubic...