If \(\alpha = \lim_{x \rightarrow \frac{\pi}{4}}\frac{\tan^{3}x - \tan x}{\cos(x + \frac{\pi}{4})}\) and \(\beta = \lim_…

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

[JEE Main 2021, 31 Aug (Shift 2)]