C# enumeration problem

In C#, I have an enumeration

    public enum Orientation
    {
        East = 1,
        West = East,
        South = 2,
        North = 3
    }

At this time, East and West has same underlying value (1) and I cannot write a switch like this

    switch (orientation)
    {
        case Orientation.East:
            Console.WriteLine("East");
            break;
            
        case Orientation.North:
            Console.WriteLine("North");
            break;
            
        case Orientation.South:
            Console.WriteLine("South");
            break;
            
        case Orientation.West:
            Console.WriteLine("West");
            break;
    }

Because when I compile, I will have an error: "The label 'case 1:' already occurs in this switch statement"

I don't understand why C# supports to declare enumeration like that. If East and West has same meaning, I will not waste my time to create both of them.

Can anybody has experience with C# help me?