Write a Python function `unique_product` that calculates the product of all unique numbers in a given list. The function should remove duplicate numbers from the list and then compute the product of the remaining numbers.
#### Example Usage
```python [main.nopy]
print(unique_product([10, 20, 30, 40, 20, 50, 60, 40])) # Output: 720000000
print(unique_product([1, 2, 3, 1])) # Output: 6
print(unique_product([7, 8, 9, 0, 1, 1])) # Output: 0
```
#### Constraints
- The input list will contain integers.
- The list may contain duplicate values.
- The product of the numbers will not exceed the range of a Python integer.