-----Description-----
Given an integer array nums, return true if there exists a triple of indices (i, j, k) such that i < j < k and nums[i] < nums[j] < nums[k]. If no such indices exist, return false.

-----Input-----
The input consists of a single list:
nums: A list of integers.

-----Output-----
The output is a boolean:
Returns true if there exists a triplet (i, j, k) where i < j < k and nums[i] < nums[j] < nums[k]; otherwise, returns false.

