Determinants & Inverses · Hard problem

A $3\times3$ matrix $A$ has columns $\mathbf c_1, \mathbf c_2, \mathbf c_3$ and $\det A = 4$. Let $B$ be the matrix with columns $\mathbf c_2 + \mathbf c_3$, $\mathbf c_3 + \mathbf c_1$, $\mathbf c_1 + \mathbf c_2$ (in that order). Find $\det B$.