Let $a$, $b$, $c$, and $d$ be distinct real numbers such that / begin{align*} a & = / sqrt{4 + / sqrt{5 + a}}, / / b & = / sqrt{4 - / sqrt{5 + b}}, / / c & = / sqrt{4 + / sqrt{5 - c}}, / / d & = / sqrt{4 - / sqrt{5 - d}}. / end{align*}Compute $abcd$.
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