To solve this inequality, we need to isolate the logarithmic term first.

First, divide both sides by 3:

log1/3 (x^2+2x) > -1/3

Next, we need to get rid of the logarithm by rewriting it as an exponential equation:

10^(-1/3) < x^2 + 2x

Now, simplify the left side by taking the cube root of 10:

0.46416 < x^2 + 2x

Subtracting 0.46416 from both sides gives:

0 < x^2 + 2x - 0.46416

Now, we need to solve for x by factoring the quadratic equation:

0 = (x + 2.154)(x - 2.154)

So, x is in the range of (-2.154, 0) U (0, 2.154).