Installing Python@3.10 Dependency: gdbm Error - 403 Forbidden

The error message indicates a failure while attempting to download the 'gdbm' dependency for Python 3.10. The requested URL returned a 403 error, signifying access to the file is forbidden. This usually occurs when Homebrew, the package manager, tries to download 'gdbm' from the Tsinghua University mirror, facing an access issue. It could be a temporary mirror problem or a system configuration issue.

To resolve this, try the following steps:

1. Update Homebrew: Run 'brew update' to ensure you have the latest Homebrew version and package definitions.

2. Retry the installation: Run 'brew install python@3.10' again. Homebrew will automatically download dependencies during the installation.

3. Use a different mirror: If the issue persists, try using a different mirror for Homebrew. Set the 'HOMEBREW_BOTTLE_DOMAIN' environment variable to a different mirror's URL before running the installation command. For example:

export HOMEBREW_BOTTLE_DOMAIN='https://dl.bintray.com/homebrew/mirror'
brew install python@3.10

Replace the URL with a known working mirror.

4. Contact the mirror provider: If the problem persists, contact the mirror provider (Tsinghua University in this case) or seek assistance from the Homebrew community. They may be able to resolve any mirror issues.

Remember to consult the official Homebrew documentation or community resources for more specific troubleshooting steps related to your system configuration.