Simple isn't enough

Calculus Level 4

\[\int_{0}^{16} { \arctan{(\sqrt{\sqrt{z} -1})} \ dz}\]

If the complex integral above can be expressed as \(a + ib\). Find the value of \(\left \lfloor{a + 10b}\right \rfloor \).

Clarification: \(i = \sqrt{-1}\).

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