Solve 3 cos t + 3 = 2 sin^2 t exactly on the interval from 0 to 2 pi.

1. Replace sin^2 t by 1 - cos^2 t so that only cosine remains. 2. The equation becomes 3 cos t + 3 = 2 - 2 cos^2 t. 3. Bringing everything to one side gives 2 cos^2 t + 3 cos t + 1 = 0. 4. That factors as (2 cos t + 1)(cos t + 1) = 0. 5. The first factor gives cos t = -1/2, whose solutions are 2 pi/3 and 4 pi/3. 6. The second factor gives cos t = -1, whose solution is pi. 7. The full solution set is 2 pi/3, 4 pi/3 and pi. 8. The angles pi/3 and 5 pi/3 correspond to cos t = +1/2 and so lose the negative sign in the first factor. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_