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The inexact value of tan 330 is -0.577350, to six significant places. The exact value cannot be represented as a single number because it is a non terminating decimal. To represent it exactly, consider that tan x is sin x over cos x, and that sin 330 is -0.5 and cos 330 is square root of 0.75. As a result, the exact value of tan 330 is -0.5 divided by square root of 0.75.
tan u/2 = sin u/1+cos u
0.34202014332566873304409961468226
The exact value is 0.5*sqrt(3)
0.4226182617