To solve the equation tan(x^2 + 2x + 3) = tan(2), we can start by setting the angles inside the tangent functions equal to each other:

x^2 + 2x + 3 = 2

Next, we can rearrange the equation to get a quadratic equation:

x^2 + 2x + 1 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. In this case, the equation can be factored as:

(x + 1)^2 = 0

Setting each factor equal to zero, we get:

x + 1 = 0

Solving for x, we find:

x = -1

Therefore, the solution to the equation tan(x^2 + 2x + 3) = tan(2) is x = -1.