To solve the inequality log1/3(x^2 + x - 3) < -2, we have to rewrite it in exponential form.

First, I will rewrite the inequality in exponential form:
1/3^(log1/3(x^2 + x - 3)) < 1/3^(-2)

Now, simplify the equation:
x^2 + x - 3 < 1/9

Now, rewrite the inequality in standard form:
x^2 + x - 3 - 1/9 < 0

x^2 + x - 3 - 1/9 < 0
x^2 + x - 28/9 < 0

Next, factor the quadratic equation:
(x + 3)(x - 8/3) < 0

Now, we find the critical points by solving for x when the expression equals 0:
x + 3 = 0 -> x = -3
x - 8/3 = 0 -> x = 8/3

Now, create a number line with the critical points and test each interval to determine the solution to the inequality.

Interval 1: (-∞, -3)
Choose x = -4:
(-4 + 3)(-4 - 8/3) = (-1)(-20/3) = 20/3 > 0

Interval 2: (-3, 8/3)
Choose x = 0:
(0 + 3)(0 - 8/3) = (3)(-8/3) = -8 < 0

Interval 3: (8/3, ∞)
Choose x = 3:
(3 + 3)(3 - 8/3) = (6)(1/3) = 2 > 0

Therefore, the solution to the inequality is x ∈ (-3, 8/3).