The x axis is when y=0

when y=0 x=0, pi/3, 2pi/3 ..... npi/3 where n is a positive integer.

So x =0 will only give 1 of the answers. And I got root3, the same as you.

When tan theta = root3 theta=pi/3 radians (angle on the right between the x axis and the tangent)

You will now need to find y' for x=pi/3. (you should get -root3 I think)

The angle will be the same but it will be on the left side. The angle between the positive side will be 2pi/3

And, you will need to convince yourself that the others are a repeat of these 2.

If you think I've done something wrong or you would like more of an explanation, just ask.

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When you are working with graphs it always makes it easier if you have the best idea possible of what the graph looks like. (Without doing too much work)

This is a sine graph (oscilating about the x axis)

with amplitude 1/root3

and period = 2pi/3

A knowledge of the graph will tell you that it will cross the x axis at 0,pi/3, 2pi/3 etc

and it will have a positive gradient at x=0 a negative one at x=pi/3 and these 2 gradients will repeat themselves with each intersection of the x axis.

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I appologize for the presentation of this answer, I don't know haw to use latex yet. I've just started learning but I am having difficulty with it.