I really need help here!

Using the triple angle identities for sin, cos and tan, Solve the equation

1.) 4x^3 - 3x = -(1/sqrt2)

At first instinct I saw that it resembled the triple angle identity for cosine so I had cos3x=-(1/sqrt2), arccos(1/sqrt2) gave me pi/4 and then cosx is pi/12. However, the answer had cos(11pi/12) and cos(5pi/12), how did they get that?

2.) Solve x^3 - 3sqrt(3)x^2 -3x + sqrt(3) = 0. I couldn't see how it represented any of the triple identities. I thought tan3x is possible but I have problems with the coefficients, they don't tally!

Please help me, thank you so very much!