solve`:sin^-1x+sin^-1 2x=pi/3`

Explanation

To solve the equation \( \sin^{-1} x + \sin^{-1} 2x = \frac{\pi}{3} \), we can use the identity for the sum of inverse sine functions. Let's go through the solution step by step.

### Step 1: Use the Identity for Sine Inverses
We know that:
\[ \sin^{-1} a + \sin^{-1} b = \sin^{-1} \left( a \sqrt{1 - b^2} + b \sqrt{1 - a^2} \right) \]
In our case, let \( a = x \) and \( b = 2x \). Therefore, we can rewrite the left-hand side:
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