Windows Authentication to make SQL Server Connection

Hello:
I have a .NET Core Web API Service which requires to connect to the SQL Server database using Windows Authentication. This is how it should work (raw):
1) The Windows username and password will be passed to the service method.
2) With the supplied username and password the service will make a trusted windows authentication to the SQL Server database.
I'm not sure how I will make use of the Windows Identity classes to build this.
Any help will be appreciated.