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 $abcd$.

M? aoc=96 ? space, m, angle, a, o, c, equals, 96, degree \qquad m \angle boc = 8x - 67^\circm? boc=8x? 67 ? space, m, angle, b, o, c, equals, 8, x, minus, 67, degree \qquad m \angle aob = 9x - 75^\circm? aob=9x? 75 ? space, m, angle, a, o, b, equals, 9, x, minus, 75, degree find m\angle bocm? bocm, angle, b, o, c: