# 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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