If \( \alpha = \displaystyle \lim_{x \to \pi/4} \dfrac{\tan^{3} x - \tan x}{\cos \left( x + \dfrac{\pi}{4} \right)} \) and \( \beta =\displaystyle \lim_{x \to 0} (\cos x)^{\cot x} \) are the roots of the equation \( ax^{2} + bx - 4 = 0 \) , then the ordered pair \( (a , b) \) is:
