tan3x=1 between 0 and 2pi

2pi in radians is the same as 360 degrees, and you have got tan 3x, so we have to triple the range; from 0 to 1080 degrees.

All we have to do then is to find the first solution, which would be arctan(1), then, we draw a CAST diagram, with the line running from the bottom left to top right quadrants, with the angle formed with the x axis being arctan(1).

Then, we go around the line created looking at the roots 3 times (as it's 3x).

There should be six roots, which we then divide by 3 to calculate what x would be.

Hope this helped!

tan 3x = 1

The tangent is equal to 1 at pi/4, 5pi/4, 9pi/4, 13pi/4, 17pi/4 and  21pi/4

Dividing each by 3 we have

pi/12, 5pi/12, 9pi/12 (3pi/4), 13pi/12, 17pi/12 and 21pi/12