E Power Eye Pie Plus One

Calculus Level 3

If the following integral equals to \(Z\)

\[ \large \displaystyle \int_0^{\pi /2} \left ( (\sin x)^{\cos x} - (\cos x)^{\sin x} \right) \mathrm{d}x \]

What is the value of \(\lfloor 1000Z \rfloor \)?

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