Question 1206427
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<pre>

Actually, tan(x) has a basic period from 0 to {{{pi}}}.


The interval from 0 to {{{2pi}}}  is TWO basic periods of tan(x).


Therefore, to simplify the problem, you could find the solutions to the given equation in the interval [0,{{{pi}}}) first,
and then to extend (to translate) the roots from this interval [0,{{{pi}}}) to one interval forward.


In the basic interval [0,{{{pi}}}), the roots are 0 and {{{3pi/4}}}.


After moving forward one period, two other roots are added to the set of solutions,  {{{pi}}}  and  {{{7pi/4}}}.
</pre>

Solved.



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Generally speaking, &nbsp;in &nbsp;Math it is not a good practice / (is not a good style) 
to ask about the solutions of the equation 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;f(x) = 0, 


where &nbsp;f(x) &nbsp;is periodical function with the period &nbsp;T, &nbsp;in two-period interval &nbsp;[0,2T).


It is not a good style.


Such questions, &nbsp;as a rule, &nbsp;go about one single period interval &nbsp;[0,T).



Otherwise, &nbsp;questions about mathematical competence of the author may arise.