Help with tangent function

Hi, here's my example from my math book that I don't understand.

Sketch the graph of y = -3 tan 2x.

By solving the equations

2x = - pi/2 and 2x = pi/2

x = -pi/2 x = pi/4

Here's the part that I have a problem understanding:

when x = - pi/8

- 3 tan 2x = 3

when x = 0

-3 tan 2x = 0

when x = pi/8

-3 tan 2x = -3

Can I do this calculation without looking at a graph. I can perform a simple x and y cordinate using this technique but when it comes to tangent problems, I can't same to apply the same principle.

Please help