Those 60° angle spots are actually two of the real physics' Lagrange Points, which are just gravitational equilibrium points between three bodies. The 60° ones are the only ones with a stable potential, which means rather than having to balance 'on the tip of the pen' to be at the perfect position, here the surrounding gravitational fields are actually like a valley that makes everything fall in and congregate in the stable area. That sounds all nice and comfy, but that is also the reason why those spots are usually inhabited by large quantities of asteroids and such, which the area literally sucks in along with any other kind of junk. Having a planet in such a position would for sure make a population face a much greater risk of impacts and eventual extinction grade catastrophic collisions. Where we are lucky to have Jupiter kinda suck out long time visitors into higher sun orbits, this here is pretty much the opposite that happily invites any kind of malicious rock around.
...Not so much optimal system now, huh?^^' Maybe when we have asteroid defense lasers.
