The Equation:
The given equation is:
cos^2(theta) - cube root of sin(theta) * cos(theta) = 0

Simplifying the Equation:
To find the general solution of the equation, let's simplify it step by step.
1. Let's rewrite the equation using trigonometric identities:
cos^2(theta) - (sin(theta) * cos(theta))^(1/3) = 0

Separating the Variables:
2. Now, let's separate the variables:
cos^2(theta) = (sin(theta) * cos(theta))^(1/3)

Squaring Both Sides:
3. To eliminate the cube root, let's square both sides of the equation:
(cos^2(theta))^2 = ((sin(theta) * cos(theta))^(1/3))^2
cos^4(theta) = sin(theta) * cos(theta)

Applying Trigonometric Identity:
4. Using the identity sin(2theta) = 2sin(theta) * cos(theta), we can rewrite the equation as:
cos^4(theta) = sin(theta) * cos(theta)
cos^4(theta) = (1/2) * sin(2theta)

Using Double Angle Formula:
5. Using the double angle formula for sine, sin(2theta) = 2sin(theta) * cos(theta), the equation becomes:
cos^4(theta) = (1/2) * 2sin(theta) * cos(theta)
cos^4(theta) = sin(theta) * cos(theta)

Substituting with Trigonometric Identity:
6. Substituting cos^2(theta) = 1 - sin^2(theta) into the equation:
(1 - sin^2(theta))^2 = sin(theta) * cos(theta)

Expanding and Rearranging:
7. Expanding and rearranging the equation:
1 - 2sin^2(theta) + sin^4(theta) = sin(theta) * cos(theta)

Using Pythagorean Identity:
8. Applying the Pythagorean identity sin^2(theta) + cos^2(theta) = 1, we can substitute 1 - cos^2(theta) for sin^2(theta):
1 - 2(1 - cos^2(theta)) + (1 - cos^2(theta))^2 = sin(theta) * cos(theta)

Simplifying the Equation:
9. Simplifying the equation:
1 - 2 + 2cos^2(theta) + 1 - 2cos^2(theta) + cos^4(theta) = sin(theta) * cos(theta)
cos^4(theta) - cos^2(theta) + 1 = sin(theta) * cos(theta)

Using Quadratic Formula:
10. Rearranging the equation to a quadratic form:
cos^4(theta) - cos^2(theta) + 1 - sin(theta) * cos(theta) = 0

General Solution:
The general solution of the equation cos^2(theta) - cube root of sin(theta) * cos(theta) = 0 is not easily obtainable using traditional mathematical techniques. It may require the use of numerical methods or approximation techniques to find the values of theta that satisfy the equation.