Problem: 'Access is denied. [0x80070005]' when changing sql server agent login

Trying to change the sql server agent to run as a non-admin user, I couldn’t get Sql Server Agent to work without giving it administrator privileges. I got:

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WMI Provider Error
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Access is denied. [0x80070005]
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OK
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You have to grant two privileges - both the Agent User and the MSSQL user.

SQLServerSQLAgentUser$bigserver$inst01
SQLServerMSSQLUser$bigserver$inst01