MainWindow.xaml

<Window x:Class="TestWpfFade.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:TestWpfFade"
        mc:Ignorable="d"
        Title="MainWindow" Height="450" Width="800"
        Opacity="0.0"
        Loaded="Window_Loaded"
        MouseDoubleClick="Window_MouseDoubleClick">
    <StackPanel>
        <TextBlock>Hello, World!!!</TextBlock>
    </StackPanel>
</Window>

MainWindow.xaml.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Animation;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using System.Windows.Threading;

namespace TestWpfFade
{
    public partial class MainWindow : Window
    {
        bool _shown = false;
        bool _animating = false;

        public MainWindow() => InitializeComponent();

        private void Fade(double from, double to)
        {
            if (_animating)
                return;

            DoubleAnimation animation = new DoubleAnimation
            {
                To = to,
                From = from,
                BeginTime = TimeSpan.FromSeconds(0),
                Duration = TimeSpan.FromSeconds(3),
                FillBehavior = FillBehavior.Stop
            };
            animation.Completed += (o, e) =>
            {
                Opacity = to;
                _shown = !_shown;
                _animating = false;
            };
            _animating = true;
            Opacity = from;
            BeginAnimation(OpacityProperty, animation);
        }

        void FlipSwitch()
        {
            Dispatcher.Invoke(DispatcherPriority.Normal, new Action(() => FlipReally()));

            void FlipReally()
            {
                if (!_shown)
                    Fade(0.0, 1.0);
                else
                    Fade(1.0, 0.0);
            }
        }

        private void Window_Loaded(object sender, RoutedEventArgs e) => FlipSwitch();
        private void Window_MouseDoubleClick(object sender, MouseButtonEventArgs e) => FlipSwitch();
    }
}