Please reason step by step, and put your final answer within \boxed{}.
Given that the vector $\vec{a}$ has a magnitude of 1, the vector $\vec{b}$ has a magnitude of 6, and the dot product of $\vec{a}$ with $\vec{b}-\vec{a}$ equals 2, find the angle between vectors $\vec{a}$ and $\vec{b}$.
user