I have a project and I don't have access to the Bitbucket repo but I have master access to the Magento Cloud project.
How could I clone the project to my local environment?
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After you log in to Magento cloud, go to your project from the top menu. On the left panel, you will the environments/branches available for the project. Click on the environment you want to clone.
After that, you will be able to see the CLI/GIT command to clone the repo from the cloud directly. Please see the below image.
Let me know if you have any questions.