When you are solving an equation like cos(3t) = - 1 / sqrt(2), you should first look at the unit circle and determine the sign and the approximate values of 3t. Use arccos only in the end to get the numerical value, and only if the the argument of cosine is not a multiple of 30 or 45 degrees.
In this case, if you draw a vertical line through x = - 1 / sqrt(2), it intersects the unit circle at 3pi/4 and 5pi/4. So,
where . This means
Now find all t from 0 to 2pi. Some of them will generate the same solution x = cos(t) to the original equation.