Access Denied when indexing sps3:// paths for People Search in SharePoint 2010

If you set a dedicated Default Content Access Account (recommended) for search indexing, you may find the following error when indexing the sps3:// path for People Search:

"Access is denied. Verify that either the Default Content Access Account has access to this repository, or add a crawl rule to crawl this repository. If the repository being crawled is a SharePoint repository, verify that the account you are using has "Full Read" permissions on the SharePoint Web Application being crawled. ( HttpStatusCode Unauthorized The request failed with HTTP status 401: Unauthorized. )"

I checked the Full Read permissions for the content access account as recommended, but these were correctly implemented. I then discovered that you have to add the content access account to the permissions of the User Profile Service Application by clicking the "Administrators" button when highlighting the User Profile SA in Central Administration.

Then, add the content access account to the list of administrators and assign it "Retrieve People Data for Search Crawlers" permissions, as shown below.

Finally, start a full crawl in search to check the problem has been resolved.