To evaluate the expression for the inverse tangent of negative square root of 3, we need to determine the angle whose tangent value equals negative square root of 3. The inverse tangent function, denoted as tan-1(x), is defined within the interval of (-π/2, π/2). This range is crucial as it restricts the possible angles we can consider.

When analyzing the unit circle, we recognize that tangent values are positive in the first quadrant and negative in the fourth quadrant. Since we are dealing with the inverse tangent of a negative value, our solution must lie in the fourth quadrant.

In the fourth quadrant, the reference angle corresponding to π/3 is -π/3. The tangent of this angle is negative square root of 3, which confirms that:

tan(-π/3) = -√3

Thus, the solution to the expression tan-1(-√3) is:

-π/3

This result indicates that the inverse tangent of negative square root of 3 is -π/3, providing a clear understanding of the relationship between the angle and its tangent value.