2cos^2(theta)-cos(theta)+3=0 appears to be the intended question.
2cos^2(theta)-cos(theta)+3=(2cos(theta)-3)(cos(theta)-1)=0.
cos(theta) cannot be greater than 1 or less than -1, so cos(theta)=3/2 can be ruled out, leaving cos(theta)=1 as the only solution. However, values of theta are countless and are given by theta=2πn where n is an integer, or 360n in terms of degrees: 0, 360, 720, etc.