Calculation of a Minimum Distance

Calculus Level 4

\[ \large \lim_{\theta \to \pi/4} {\frac{{\mathop {(\cos \theta )}\nolimits^{\frac{{\sin \theta }}{{\cos \theta - \sin \theta }}} }}{{\mathop {(\sin \theta )}\nolimits^{\frac{{\cos \theta }}{{\cos \theta - \sin \theta }}} }}} = a \sqrt b \]

If the equation above holds true for square-free positive integer \(b\), find \(\lfloor a \rfloor +b \).

Notations: \( \lfloor \cdot \rfloor \) denotes the floor function.

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