What is the value of [math] \displaystyle \lim_{x \to \tfrac{\pi}{3}} \frac{\sin\left(x-\tfrac{\pi}{3}\right)}{1 - 2 \cos x} [/math]?
What is the value of [math]x[/math] where [math]x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)[/math] and [math](1+\tan x)(1-\tan x)\sec^2 x+2^{tan^2 x}=0[/math]?