Given an array of integers, nums, determine the number of triplets of distinct indices (i, j, k) that can be selected from the array such that the values at those indices can form the sides of a valid triangle.
Return this count as the result.
Note: The triplet of indices is treated as an unordered combination, not a permutation. For example, indices (0, 1, 2) and (2, 1, 0) represent the same triplet and should be counted once.
Constraints:
The solution uses the sort and search pattern ...