To rearrange the equation for o, the original equation is transformed into a quadratic form by substituting x = tan(o/2), resulting in (1/6)x^2 + (1/2)x = t. This simplifies to the quadratic equation x^2 + 3x - 6t = 0. The next step involves solving this quadratic equation for x in terms of t using the quadratic formula. Once x is determined, o can be found by taking the arctangent and adjusting for the original substitution. The discussion emphasizes the importance of correctly applying algebraic manipulation to solve for the desired variable.
