Please solve the programming task below using a self-contained code snippet in a markdown code block.

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 exists, return false.
 
Please complete the following python code precisely:
```python
class Solution:
    def increasingTriplet(self, nums: List[int]) -> bool:
```