If `acos^2theta+3acostheta sin^2theta=m` and `asin^3theta+3acos^2thetasintheta=n`. , then prove that: `(m+n)^(2//3)+(m-n)^(2//3)=2a^(2//3)`

Explanation

To prove that \((m+n)^{\frac{2}{3}} + (m-n)^{\frac{2}{3}} = 2a^{\frac{2}{3}}\), we start with the given expressions for \(m\) and \(n\):

1. **Given:**
\[ m = a \cos^2 \theta + 3a \cos \theta \sin^2 \theta \]
\[
n = a \sin^3 \theta + 3a \cos^2 \theta \sin \theta
...