from fastapi import APIRouter, HTTPException

users = [
    {
        "id": "1",
        "username": "admin",
        "password": "securepassword"
    }
]

router = APIRouter()

@router.get("/auth")
async def authenticate_user(
    username: str = "admin",
    password: str = "securepassword"
):
    """authenticates the user"""
    if request.method != "GET":
        raise HTTPException(status_code=405, detail={
            "message": "Method Not Allowed",
            "method": request.method,
            "_verb": "get"
        })

    user = next((u for u in users if u["username"] == username), None)
    if not user or user["password"] != password:
        raise HTTPException(status_code=400, detail={
            "message": "Invalid credentials",
            "method": "GET",
            "_verb": "get"
        })

    return {
        "message": "Authentication successful",
        "user": username,
        "method": "GET", 
        "_verb": "get"
    }
```

This endpoint authenticates a user by checking the provided username and password against a hardcoded list of users. It follows the rules and examples provided:

- It uses the `@router.get` decorator for a GET method
- It raises a 405 Method Not Allowed error if the request method is not GET
- It raises a 400 Bad Request error if the username/password is invalid
- The response includes the "method": "GET" and "_verb": "get" fields
- It maintains the expected response structure from the examples

Note that this is just a simple example, and in a real application, you would likely use a more secure authentication method and store user data in a proper database.