Find the set of values of parameter `a` so that the equation `(sin^(-1)x)^3+(cos^(-1)x)^3=api^3` has a solution.

Explanation

To solve the equation \((\sin^{-1} x)^3 + (\cos^{-1} x)^3 = a \pi^3\) and find the set of values of the parameter \(a\) such that the equation has a solution, we can follow these steps:

### Step 1: Use the identity for the sum of cubes
Recall that the sum of cubes can be expressed as:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
Let \(a = \sin^{-1} x\) and \(b = \cos^{-1} x\). Then we can rewrite the left-hand side:
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