Find all the angles between 0 and, 720 whose tangent is 1/ �ã 3

Answer 1

Do you mean 1/(sqrt3) ?
The first such angle is 30 degrees. (Think of a right triangle with sides of 1, 2 and sqrt 3, with 2 being the hypotenuse. Its smallest angle is 30 degrees.)

The angle in the third quadrant which has a reference angle of of 30 degrees (from the -x axis) is 210 degrees, and that angle has the same tangent. Add 360 degrees to those angles and you get two more: 390 and 570 degrees.