I need help to optimize a function

Basically I want to generate a an angle (0 - 360 degrees) that isn't within a specified range of a number of other angles. I already made this function to check two angles:

function check(angle1, angle2, range) {
    var diff = angle1 - angle2;

    if(Math.abs(diff % 360) <= range || (360-Math.abs(diff % 360)) <= range) {
        return true;
    } else {
        return false;
    }
}

Simple enough, but I need to check a random angle against all other angles, proceed if it passes, generate a new angle and recheck if it fails, and recognise when it's not possible for any new angle to pass.

I think this would work:

var others = [array of objects];

...

for(var i = 0; i < 360; i++) {
    var pass = true;
    for(var n = 0; n < others.length; n++) {
        if(check(i, others[n].angle, 5)) {
            pass = false;
            break;
        }
    }
    if(pass) return i;
}

return false;

However that is a lot of looping and I would much prefer a random angle rather than incrementing. Is there a faster and better way to do this? Thanks.

Edit: decided to do something like this, got the idea from @TheBronx's answer.

var angles = [];

var range = 5;

function alterAngle(a, n) {
  var angle = a + n;
  if(angle < 0) angle = 360 + angle;
  if(angle > 360) angle = angle - 360;
  return angle;
}

// in the function

var angle = Math.floor(Math.random() * 360);

if(angles.indexOf(angle) == -1) {
  for(var i = -range; i <= range; i++)
    angles.push(alterAngle(angle, i));
}

---

Idea. Imagine your angles are cards in a deck. Once you generate a random angle, you remove that angle from the deck, and also the angles within your range. When you have to generate a new angle, instead of generating a random between 0..360 you just have to "pick a card". This will always work, unless you don't have more "cards" available.

The problem is, do you have a lot of cards? Do you have enough time to initialize the "cards" at start?

Just an idea... Don't know if it is good or not but seems promising.