This is a polynomial of the third degree which can be solved as follows:
let tan(x) =y
dividing the equation by 3 (the coefficient of the highest power)
the last term (+1/3) is the product of the three roots of the equation. This means that the roots should contain the value 1.
dividing the equation by (y-1)
then the above equation will be
the second bracket can be solved by the known equation of solving quadratic equations
the root are 1,1/root(3),-1/root(3)