To solve the expression given, we first simplify each part.

The expression to evaluate is:

\[
\frac{\sqrt{3}}{3} + \frac{1 - \sqrt{3}}{1 + \sqrt{3} + 1}
\]

1. **Simplifying the second fraction**:
\[
\frac{1 - \sqrt{3}}{1 + \sqrt{3} + 1} = \frac{1 - \sqrt{3}}{2 + \sqrt{3}}
\]

2. **Rationalizing the denominator**:
To simplify this fraction, we can multiply the numerator and denominator by the conjugate of the denominator:
\[
\frac{(1 - \sqrt{3})(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})}
\]

Calculating the denominator:
\[
(2 + \sqrt{3})(2 - \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1
\]

Now for the numerator:
\[
(1 - \sqrt{3})(2 - \sqrt{3}) = 2 - \sqrt{3} - 2\sqrt{3} + 3 = 5 - 3\sqrt{3}
\]

Therefore, we have:
\[
\frac{1 - \sqrt{3}}{2 + \sqrt{3}} = 5 - 3\sqrt{3}
\]

3. **Combining both fractions**:
Now we substitute back into the expression:
\[
\frac{\sqrt{3}}{3} + \frac{5 - 3\sqrt{3}}{1}
\]

This simplifies to:
\[
\frac{\sqrt{3}}{3} + 5 - 3\sqrt{3}
\]

4. **Finding a common denominator**:
To combine these, we can write \(5\) and \(-3\sqrt{3}\) in terms of the common denominator \(3\):
\[
\frac{\sqrt{3}}{3} + \frac{15}{3} - \frac{9\sqrt{3}}{3} = \frac{\sqrt{3} + 15 - 9\sqrt{3}}{3} = \frac{15 - 8\sqrt{3}}{3}
\]

Thus, the final result is:
\[
\frac{15 - 8\sqrt{3}}{3}
\]