Unique Triplets Sum to Target

Unity's runtime tooling may need to identify combinations of three values that satisfy a target constraint. Given an integer array nums and an integer target, return every unique triplet [a, b, c] such that a + b + c == target.

Each triplet must use three different array positions, and the result must not contain duplicate value combinations. Return triplets in nondecreasing order, with the complete result sorted lexicographically. If no triplet exists, return an empty list.

Formal Specification

Implement three_sum_target(nums, target).

• Input: nums, a list of integers, and target, an integer.
• Output: a list of three-element lists containing all unique value triplets whose sum equals target.
• The input array may contain duplicate values and negative numbers.
• The input list may be reordered during processing.