To solve this inequality, we need to isolate x on one side of the inequality sign.

Subtracting tg x from both sides, we have:

x^2 + 2x > 3

Now, subtracting 3 from both sides:

x^2 + 2x - 3 > 0

Next, we need to factor the quadratic expression:

(x + 3)(x - 1) > 0

Now, we need to determine the sign of the expression. We can do this by plotting the critical points on a number line:

x = -3, x = 1.

Now, test a point in each interval into the inequality to determine the sign of the expression:

For x < -3, test x = -4:
(-4 + 3)(-4 - 1) = (-1)(-5) = 5, which is positive.

For -3 < x < 1, test x = 0:
(0 + 3)(0 - 1) = (3)(-1) = -3, which is negative.

For x > 1, test x = 2:
(2 + 3)(2 - 1) = (5)(1) = 5, which is positive.

Therefore, the solutions to the inequality are x < -3 and x > 1.