<Storyboard>
    <DoubleAnimationUsingKeyFrames Storyboard.TargetProperty="(UIElement.RenderTransform).(CompositeTransform.Rotation)" Storyboard.TargetName="grid">
        <EasingDoubleKeyFrame KeyTime="0" Value="0"/>
        <EasingDoubleKeyFrame KeyTime="0:0:0.3" Value="60"/
    </DoubleAnimationUsingKeyFrames>
</Storyboard>

var turnSB = new Storyboard();

var doubleAnim = new DoubleAnimationUsingKeyFrames();
doubleAnim.KeyFrames.Add(new EasingDoubleKeyFrame() { KeyTime = TimeSpan.FromMilliseconds(0), Value = currentAngle });
doubleAnim.KeyFrames.Add(new EasingDoubleKeyFrame() { KeyTime = TimeSpan.FromMilliseconds(500), Value = targetAngle });

turnSB.Children.Add(doubleAnim);

Storyboard.SetTarget(doubleAnim, this.RenderTransform);
Storyboard.SetTargetProperty(doubleAnim, "(CompositeTransform.Rotation)");

turnSB.Begin();

Storyboard.SetTargetProperty(doubleAnim, "(UIElement.RenderTransform).(CompositeTransform.Rotation)");

Storyboard.SetTarget(doubleAnim, this.RenderTransform);
Storyboard.SetTargetProperty(doubleAnim, "Rotation"); // maybe "CompositeTransform.Rotation"
storyboard.Children.Add(doubleAnim);