To solve the equation cos(theta)/sin(theta) = 10.11, it can be rewritten as tan(theta) = 1/10.11. Taking the arctangent of both sides provides the value of theta within the interval (0, π/2). The user confirmed the method by using an acot scientific calculator, which yielded consistent results. The discussion highlights a common trigonometric identity and the process of solving for theta. The solution emphasizes the importance of understanding cotangent and tangent relationships in trigonometry.