Key Fixes:
Handling the Circular Nature: Updated the logic for insert_nth and delete_nth to correctly handle the circular references, particularly when inserting or deleting at the head or tail.
Updating Tail Properly: Ensured that the tail is correctly updated when inserting or deleting at the end of the list.
Edge Cases: Improved handling of edge cases, like when the list has only one node.
Testing:
The test_circular_linked_list function will run through various cases to validate that the circular linked list behaves as expected. You can run the script to ensure everything works correctly.

Let me know if you encounter any other issues!

Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".