Semi-transparent window in GTK# (Mono, C#)

GtkDimScreen.cs

using System;
using System.Reflection;
using System.Runtime.InteropServices;
using Cairo;
using Gtk;

public class GtkDimScreen
{
	private DrawingArea drawingArea;
	
	public static void Main ()
	{
		new GtkDimScreen();
	}
	
	public GtkDimScreen()
	{
		Application.Init ();
		var window = new Gtk.Window ("Invisible sandwich");
		// Turn off title bar
		window.Decorated = false;
		
		// Create Cairo drawing area
		drawingArea = new DrawingArea();
		drawingArea.ScreenChanged += OnScreenChanged;
		drawingArea.ExposeEvent += OnExposeEvent;
		
		// Add drawing area to window
		var box = new HBox (true, 0);
		box.Add (drawingArea);
		window.Add (box);
		window.ShowAll ();
		window.Maximize();
		
		Application.Run ();
	}
	
	protected void OnScreenChanged(object o, ScreenChangedArgs args)
	{
		// Use the RGBA colour map, so that alpha values work
		drawingArea.Screen.DefaultColormap = drawingArea.Screen.RgbaColormap;
	}
	
	protected void OnExposeEvent(object o, ExposeEventArgs args)
	{
		using (Context ctx = Gdk.CairoHelper.Create(drawingArea.GdkWindow))
		{
			// Paint a semitransparent colour onto the background
			ctx.SetSourceRGBA(0, 0, 0, 0.4);
			ctx.Operator = Operator.Source;
			ctx.Paint();
		}
	}
}

can you telll me how to add widget in that transparent area