My favourite problem ever

Algebra Level 3

If \(a,b,c,d\) satisfy the equations

\(a+7b+3c+5d=0\),
\(8a+4b+6c+2d=-16\),
\( 2a+6b+4c+8d=16\),
\(5a + 3b+ 7c + d = -16 \),

find the value of \((a+d)(b+c) \).

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