Fade tabs

Main.xaml

<Grid
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
  <Grid.Resources>
    <Storyboard x:Key="ShowAnim" AccelerationRatio="0.5" DecelerationRatio="0.5">
      <DoubleAnimation Storyboard.TargetName="Tabs" Storyboard.TargetProperty="RenderTransform.X" To="0" Duration="0:0:0.2"/>
    </Storyboard>
    <Storyboard x:Key="HideAnim" AccelerationRatio="0.5" DecelerationRatio="0.5">
      <DoubleAnimation Storyboard.TargetName="Tabs" Storyboard.TargetProperty="RenderTransform.X" To="-340" Duration="0:0:0.2"/>
    </Storyboard>
    <DataTemplate x:Key="TabHeader">
      <DataTemplate.Resources>
        <Storyboard x:Key="ToggleShow">
          <ObjectAnimationUsingKeyFrames Storyboard.TargetName="Show" Storyboard.TargetProperty="Visibility">
            <DiscreteObjectKeyFrame KeyTime="0" Value="{x:Static Visibility.Visible}"/>
          </ObjectAnimationUsingKeyFrames>
          <ObjectAnimationUsingKeyFrames Storyboard.TargetName="Hide" Storyboard.TargetProperty="Visibility">
            <DiscreteObjectKeyFrame KeyTime="0" Value="{x:Static Visibility.Collapsed}"/>
          </ObjectAnimationUsingKeyFrames>
        </Storyboard>
        <Storyboard x:Key="ToggleHide">
          <ObjectAnimationUsingKeyFrames Storyboard.TargetName="Show" Storyboard.TargetProperty="Visibility">
            <DiscreteObjectKeyFrame KeyTime="0" Value="{x:Static Visibility.Collapsed}"/>
          </ObjectAnimationUsingKeyFrames>
          <ObjectAnimationUsingKeyFrames Storyboard.TargetName="Hide" Storyboard.TargetProperty="Visibility">
            <DiscreteObjectKeyFrame KeyTime="0" Value="{x:Static Visibility.Visible}"/>
          </ObjectAnimationUsingKeyFrames>
        </Storyboard>
      </DataTemplate.Resources>
      <Grid>
        <ContentPresenter x:Name="Show" Content="{TemplateBinding Content}"/>
        <ContentPresenter x:Name="Hide" Content="{TemplateBinding Content}" Visibility="Collapsed"/>
      </Grid>
      <DataTemplate.Triggers>
        <DataTrigger Binding="{Binding IsSelected, RelativeSource={RelativeSource AncestorType=TabItem}}" Value="False">
          <DataTrigger.EnterActions>
            <BeginStoryboard Storyboard="{StaticResource ToggleShow}"/>
          </DataTrigger.EnterActions>
        </DataTrigger>
        <EventTrigger SourceName="Show" RoutedEvent="MouseDown">
          <BeginStoryboard Storyboard="{StaticResource ToggleHide}"/>
          <BeginStoryboard Storyboard="{StaticResource ShowAnim}"/>
        </EventTrigger>
        <EventTrigger SourceName="Hide" RoutedEvent="MouseDown">
          <BeginStoryboard Storyboard="{StaticResource ToggleShow}"/>
          <BeginStoryboard Storyboard="{StaticResource HideAnim}"/>
        </EventTrigger>
      </DataTemplate.Triggers>
    </DataTemplate>
  </Grid.Resources>
  <TabControl x:Name="Tabs" Width="400" TabStripPlacement="Right" HorizontalAlignment="Left">
    <TabControl.RenderTransform>
      <TranslateTransform X="-340"/>
    </TabControl.RenderTransform>
    <TabItem Header="Tab 1" HeaderTemplate="{StaticResource TabHeader}">
      <Ellipse Margin="10" Fill="LightBlue"/>
    </TabItem>
    <TabItem Header="Tab 2" HeaderTemplate="{StaticResource TabHeader}">
      <Ellipse Margin="10" Fill="Salmon"/>
    </TabItem>
    <TabItem Header="Tab 3" HeaderTemplate="{StaticResource TabHeader}">
      <Ellipse Margin="10" Fill="LightGreen"/>
    </TabItem>
  </TabControl>
</Grid>