1. In league with：和……联合，与……勾结，密谋，与……沆瀣一气
How could you be league with the mean man like him？
People are in league with one another, but not in conflict.
If you are in league with the stones of the field, the beasts in the field will be at peace with you.
Little people often were in league with other.
2. In collaboration with：与 ……勾结；与……合作
China is developing in collaboration with the west.
Greatest grade is the result of that the departments of collaboration with one another.
In collaboration with the related organization, the plan worked well.
3. In collusion with：串通，与……勾结
The media can’t imagine the officials are in collusion with the criminals in this event.
It is obvious that she was in collusion with the defendant.
Public suffered a lot when the officials and the businesses are in collusion with each other to control the market.
The real villain was you, in collusion with him in murdering the poor guy.
The key is that the official is honest, or complicit with the man.
Her friends, her colleagues are complicit in such huge lie.
Nobody but Tom knew that he is complicit in this terrorist attack.
Complicit crime was considered as the divide of responsibility, but in fact, it’s not.