How should I calculate the determinant? $\left|\begin{array}{cccc}1&a&b&c+d\\1&b&c&a+d\\1&c&d&a+b\\1&d&a&b+c\end{array}\right|=
\left|\begin{array}{cccc}1&a&b&c\\1&b&c&a\\1&c&d&a\\1&d&a&b\end{array}\right|+
\left|\begin{array}{cccc}1&a&b&d\\1&b&c&d\\1&c&d&b\\1&d&a&c\end{array}\right|$
I tried to calculate the determinant but I couldn't do it after separating the determinant by the property.  How should I calculate it?  

Compute
$$
\begin{bmatrix}
1 & a & b & c+d \\
1 & b & c & d+a \\
1 & c & d & a+b \\
1 & d & a & b+c
\end{bmatrix}
\begin{bmatrix}
a+b+c+d \\ -1 \\ -1 \\ -1
\end{bmatrix}
$$
