sin(t)>(\sqrt(3))/(2) inequation

Given the inequality:
$$\sin{\left(t \right)} > \frac{\sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{\sqrt{3}}{2}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n + \frac{\pi}{3}$$
$$t = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
This roots
$$t_{1} = 2 \pi n + \frac{\pi}{3}$$
$$t_{2} = 2 \pi n + \frac{2 \pi}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$t_{0} < t_{1}$$
For example, let's take the point
$$t_{0} = t_{1} - \frac{1}{10}$$
=
$$\left(2 \pi n + \frac{\pi}{3}\right) + - \frac{1}{10}$$
=
$$2 \pi n - \frac{1}{10} + \frac{\pi}{3}$$
substitute to the expression
$$\sin{\left(t \right)} > \frac{\sqrt{3}}{2}$$
$$\sin{\left(2 \pi n - \frac{1}{10} + \frac{\pi}{3} \right)} > \frac{\sqrt{3}}{2}$$

                            ___
   /  1    pi         \   \/ 3 
sin|- -- + -- + 2*pi*n| > -----
   \  10   3          /     2  
                          

Then
$$t < 2 \pi n + \frac{\pi}{3}$$
no execute
one of the solutions of our inequality is:
$$t > 2 \pi n + \frac{\pi}{3} \wedge t < 2 \pi n + \frac{2 \pi}{3}$$

         _____  
        /     \  
-------ο-------ο-------
       t1      t2