2cos 4theta + 1 = 0

i know how to find the degrees (the last step of the problem), but i don't know how to start the problem. Could someone please show me the steps?

I assume you mean cos (4 theta) and not
(cos theta)^4

cos (4 theta) = -1/2
The angles with a cosine equal to -1/2 are: 120 and 240 degrees, and also 480 and 600 degrees, and 840 and 960 degrees etc (Just adding 360 degrees to previous answers). . Since that is 4 theta, divide any of those numbers by 4 for theta values that are solutions.
THETA = 30, 60, 120, 150, 210, 240...degrees