Question 358878
{{{tan (x/3) = sqrt(3)}}},
{{{(tan (x/3))^2 = 3}}},after both sides.
{{{1+(tan (x/3))^2 = 4}}},
{{{(sec (x/3))^2 = 4}}}, by a Pythagorean identity.
{{{(cos(x/3))^2 = 1/4}}}, after taking reciprocals.
{{{cos(x/3) = 1/2}}} or{{{cos(x/3) =- 1/2}}}.
The first equation gives {{{x/3 = pi/3}}}, the second {{{x/3 = (4*pi)/3}}}.
further simplification gives {{{x = pi}}} and {{{x = 4*pi}}}.  The second answer is not acceptable, therefore the final answer is {{{x = pi}}}.