Need help with sketching the graph of a tangent function

The example says:

Sketch the graph of y = -3 tan 2x

Solution:

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

x = -pi/4 x = pi/4

This part I got ok. The example goes on to sahy that between these two asymptotes, plot a few points, including the x-intercetp. it uses a short table like the one below.

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 work this like an algebra problem? or do I have to look at the unit circle and match up -pi/8 = 3 etc.?