Write the following function in the simplest form: `tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))`

Explanation

To simplify the function \( \tan^{-1}\left(\frac{3a^2x - x^3}{a^3 - 3ax^2}\right) \), we will follow these steps:

### Step 1: Substitute \( x = a \tan(\theta) \)

Let \( x = a \tan(\theta) \). This substitution helps to express the function in terms of \( \theta \).

### Step 2: Rewrite the expression

...