What you can do if you want to be exact is

http://en.wikipedia.org/wiki/Rejection_sampling. But might be inefficient as hell, also because there are not enough values at the edge.

RS is a technique to sample from a distribution, starting from another one which is easy to sample. Given you know the density between those two. And the density has an upper limit.

In your case, you can easily sample from your distribution which is approximately Gaussian, by the technique Titandrake already mentioned: Just draw the sample at a random index.

Your target distribution is uniform.

You also know the (approximate) density between those two: phi(x) := 1/sqrt(2pisigma²)exp(-x²/sigma²). On a bounded intervall, it is also bounded (but the constant might be bad, which would make the algo inefficient). Call the constant M.

So what you do to draw one sample:

1.) Draw uniform sample z from distribution x:

2.) accept z with probability phi(z)/M. Otherwise, goto 1)

To draw 1/3N samples, you do this 1/3N times.