trigonometric question

Since tan y = √3
y = π/3, 4π/3 ,7π/3 ,10π/3 ,13π/3 ,16π/3 ,19π/3 ,22π/3
By substituting y = 4x, you get the same answer.
For the first answer π/3 (i.e. 60 degrees), you have to remember it, because this is a number always appearing and it is some integral proportion of 180 degrees (or 1 radian). We also call this "special angles". Others you need to remember includes tan y = 1/√3 ==> y = π/6; and tan y = 1 ==> y = π/4.
With this in mind, and notice that the tangent curve always repeat itself every 180 degrees (1 radian), you will know the following solutions:
4π/3 (i.e. π/3 + π), 7π/3 (i.e. π/3 + 2π), and so on.

Finally, if you don't want to remember too many sin, cos and tan, you can just remember the sin and cos value of special angles, and then calculate tan y by sin y / cos y. For example, sin (π/3) = √3 / 2, cos (π/3) = 1 / 2, thus tan (π/3) = (√3 / 2) / (1 / 2) = √3.

First recall the memories on special angles.
sin 0 = 0, sin π/6 = 0.5, sin π/4 = 0.5*√2, sin π/3 = 0.5*√3, sin π/2 = 1
cos π/2 = 0, cos π/3 = 0.5, cos π/4 = 0.5*√2, cos π/6 = 0.5*√3, cos 0 = 1
tan 0 = 0, tan π/6 = 1/3*√3, tan π/4 = 1, tan π/3 = √3, tan π/2 = undefined
thus, it is obvious that 4x = π/3

Then in Adanced Maths, radian is always used to solve problems,
remember π radian = 180 degrees. Also the degree range is no longer between 0-90 degree, but a whole circle from 0-360 degree.
As Tangent is a periodic function, with period = π rad.
that's why, 4x=π/3 ,4π/3 ,7π/3 ,10π/3 ,13π/3 ,16π/3 ,19π/3 ,22π/3
(This is actually the concept of general solutions)
(tan y = nπ + k, where k is the principle angle, n is a natural number)