Limits Continuity And Differentiability

If \(\alpha = \mathop {\lim }\limits_{x \to {\pi \over 4}} {{{{\tan }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}\) and \(\beta = \mathop {\lim }\limits_{x \to 0 } {(\cos x)^{\cot x}}\) are the roots of the equation, ax² + bx \(-\) 4 = 0, then the ordered pair (a, b) is :