tgx>3/3 inequation

Given the inequality:
$$\tan{\left(x \right)} > 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\tan{\left(x \right)} = 1$$
Solve:
Given the equation
$$\tan{\left(x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
$$x_{1} = \pi n + \frac{\pi}{4}$$
$$x_{1} = \pi n + \frac{\pi}{4}$$
This roots
$$x_{1} = \pi n + \frac{\pi}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\pi n + \frac{\pi}{4}\right) + - \frac{1}{10}$$
=
$$\pi n - \frac{1}{10} + \frac{\pi}{4}$$
substitute to the expression
$$\tan{\left(x \right)} > 1$$
$$\tan{\left(\pi n - \frac{1}{10} + \frac{\pi}{4} \right)} > 1$$

   /  1    pi       \    
tan|- -- + -- + pi*n| > 1
   \  10   4        /    

Then
$$x < \pi n + \frac{\pi}{4}$$
no execute
the solution of our inequality is:
$$x > \pi n + \frac{\pi}{4}$$

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       x1