How to solve tan3x=0

Tan(x)  = 0    at  x =  0, pi, 2pi, 3pi, 4pi, 5pi and 6pi

So, dividing these by 3 we have

Tan(3x)  = 0   at x = 0, pi/3, 2pi/3, pi, (4/3)pi, (5/3)pi and 2pi if we constrain x to lie in [0, 2pi ]

A more general solution is that x = (pi/3)n   where n is an integer

tan is sin/cos  It will be 0 when sin is zero.  This is at 0, pi, 2pi, 3pi, etc

so

3x=0, pi, 2pi, 3pi, etc

x=0, pi/3, 2pi/3, pi,4pi/3, 5pi/3  etc