Question

$\tan( \frac{\pi}{3} - 4x ) = - 1$​

Answer 1

$\sf \displaystyle tg(\frac{\pi}{3}-4x)=-1\\\frac{\pi}{3}-4x=- \frac{\pi}{4}+\pi k, k\in Z\\-4x=-\frac{\pi}{4}-\frac{\pi}{3}+\pi k,k\in Z\\\\-4x=-\frac{7\pi}{12}+\pi k,k\in Z|:(-4)\\x=\frac{7}{48}-\frac{\pi k}{4},k\in Z\\\\ \boxed{x=\frac{7}{48}-\frac{\pi k}{4},k\in Z}$