<s>[INST] How to Simplify $-\frac14\sin\frac x4 + \frac{\sqrt{3}}4\cos\frac x4 = 0$? A problem requires finding the value of x, such that 
$$-\frac14\sin\frac x4 + \frac{\sqrt{3}}4\cos\frac x4 = 0$$
The site reduces the problem to $\tan(\frac x4) = \sqrt{3}$.
How one should do this? 
 [/INST] $$-\frac { 1 }{ 4 } \sin  \frac { x }{ 4 } +\frac { \sqrt { 3 }  }{ 4 } \cos  \frac { x }{ 4 } =0\\ -\frac { 1 }{ 2 } \left( \frac { 1 }{ 2 } \sin  \frac { x }{ 4 } -\frac { \sqrt { 3 }  }{ 2 } \cos  \frac { x }{ 4 }  \right) =0\\ \frac { 1 }{ 2 } \sin  \frac { x }{ 4 } -\frac { \sqrt { 3 }  }{ 2 } \cos  \frac { x }{ 4 } =0\\ \cos { \frac { \pi  }{ 3 } \sin { \frac { x }{ 4 } -\sin { \frac { \pi  }{ 3 }  } \cos { \frac { x }{ 4 } =0 }  }  } \\ \sin { \left( \frac { x }{ 4 } -\frac { \pi  }{ 3 }  \right) =0 } \\ x=\frac { 4\pi  }{ 3 } +4k\pi ,k\epsilon  \mathbb{Z}  $$
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