cot(x/4)<1 inequation

Given the inequality:
$$\cot{\left(\frac{x}{4} \right)} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\cot{\left(\frac{x}{4} \right)} = 1$$
Solve:
$$x_{1} = \pi$$
$$x_{1} = \pi$$
This roots
$$x_{1} = \pi$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \pi$$
=
$$- \frac{1}{10} + \pi$$
substitute to the expression
$$\cot{\left(\frac{x}{4} \right)} < 1$$
$$\cot{\left(\frac{- \frac{1}{10} + \pi}{4} \right)} < 1$$

   /1    pi\    
tan|-- + --| < 1
   \40   4 /    

but

   /1    pi\    
tan|-- + --| > 1
   \40   4 /    

Then
$$x < \pi$$
no execute
the solution of our inequality is:
$$x > \pi$$

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       x1