To find the default stylesheet, find the jfxrt.jar file on your computer, open it in an archiver such as WinRAR, and open com/sun/javafx/scene/control/skin/caspian.css . With this knowledge, you can easily see what may be there that is causing the problem.
caspian.css also available online, here is a link to JavaFX 2.2 .
Now add this style:
.tab-pane .headers-region { -fx-effect: null; }
It removes the default style and the shadows disappear.
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