The identity you provided relates the cotangents of the angles of triangle \( ABC \) to the lengths of its sides and the area of the triangle. The equation can be written as:

\[
\cot A + \cot B + \cot C = \frac{AB^2 + AC^2 + BC^2}{4S_{ABC}}
\]

where:
- \( A, B, C \) are the angles of the triangle at vertices \( A, B, C \),
- \( AB, AC, BC \) are the lengths of the sides opposite to the angles \( C, B, A \) respectively,
- \( S_{ABC} \) is the area of triangle \( ABC \).

This relation can be useful in various geometric proofs and calculations involving triangles. If you have any specific questions about this identity or its applications, feel free to ask!