Let $\vec a=a_1\hat i+a_2\hat j+a_3\hat k$ and $\vec b=b_1\hat i+b_2\hat j+b_3\hat k$ be two vectors such that $|\vec a|=1,\ \vec a\cdot\vec b=2$ and $|\vec b|=4$. If $\vec c=2(\vec a\times\vec b)-3\vec b$, then the angle between $\vec b$ and $\vec c$ is: