Question 922044
We know that {{{tan(30^o)=1/sqrt(3)=sqrt(3)/3}}} ,
and if we are expected to measure angles in radians,
{{{tan(pi/6)=1/sqrt(3)=sqrt(3)/3}}} , so we have one solution, {{{highlight(x=pi/6))}}} .
We also know that tangent is a function with a period of {{{pi}}} ,
and as {{{pi/6+pi=7pi/6}}} ,
{{{tan(pi/6)=tan(pi/6+pi)=tan(7pi/6)}}} ,
so {{{highlight(x=7pi/6)}}} is another solution.
There are no other solutions.
There are infinity of other angles with the same tangent,
such as {{{-5pi/6=pi/6-pi}}} or {{{13pi/6=pi/6+2pi}}} ,
but those are not in the interval {{{0<=x<=2pi}}}