These spots, known as Lagrange points, are 120 degrees in front of and behind whichever body is smaller. The discovered co-orbiting planets, located in the four-planet system KOI-730, are always 120 degrees apart, permanent fixtures in each others’ night skies.
From the link in the linked article.
http://www.newscientist.com/article/dn20160-two-planets-found-sharing-one-orbit.html?DCMP=OTC-rss&nsref=online-news
Gravitational "sweet spots" make this possible. When one body (such as a planet) orbits a much more massive body (a star), there are two Lagrange points along the planet's orbit where a third body can orbit stably. These lie 60 degrees ahead of and 60 degrees behind the smaller object. For example, groups of asteroids called Trojans lie at these points along Jupiter's orbit.
Which is it, 60 or 120 degrees? I can't finish my school project until I find out!
They are some times collectively referred to as Trojan asteroids.
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
L2 and L3 are 60 degrees ahead or behind the most massive object.
And I see someone has already explained L4 and L5 lagrange points.