Write a function `extract_even` that takes a nested tuple of integers and removes all odd numbers from it. The function should preserve the structure of the nested tuple while only retaining even numbers.
#### Example Usage
```python [main.nopy]
print(extract_even((4, 5, (7, 6, (2, 4)), 6, 8)))
# Output: (4, (6, (2, 4)), 6, 8)
print(extract_even((5, 6, (8, 7, (4, 8)), 7, 9)))
# Output: (6, (8, (4, 8)))
print(extract_even((5, 6, (9, 8, (4, 6)), 8, 10)))
# Output: (6, (8, (4, 6)), 8, 10)
```
#### Constraints
- The input will always be a tuple.
- The tuple can contain integers or other nested tuples.
- The function should handle arbitrarily nested tuples.