**Solution:**

To solve the expression **sin^3 10 sin^3 250 sin^3 310**, we can use the trigonometric identity **sin 3θ = 3sinθ - 4sin^3θ**.

Let's break down the solution step by step:

1. Convert degrees to radians: We need to convert the angles 10°, 250°, and 310° to radians. Since 1° = π/180 radians, we have:
- 10° = 10π/180 radians
- 250° = 250π/180 radians
- 310° = 310π/180 radians

2. Apply the trigonometric identity: Using the identity **sin 3θ = 3sinθ - 4sin^3θ**, we can rewrite the expression as:
- sin^3 10 sin^3 250 sin^3 310 = (sin 3(10π/180)) (sin 3(250π/180)) (sin 3(310π/180))

3. Apply the trigonometric identity for sin 3θ: We can rewrite each term using the identity **sin 3θ = 3sinθ - 4sin^3θ**:
- sin 3(10π/180) = 3sin(10π/180) - 4sin^3(10π/180)
- sin 3(250π/180) = 3sin(250π/180) - 4sin^3(250π/180)
- sin 3(310π/180) = 3sin(310π/180) - 4sin^3(310π/180)

4. Calculate the values of sin(θ) for each angle: Using the sine function, we can find the values of sin(10π/180), sin(250π/180), and sin(310π/180) using a calculator or trigonometric tables.

5. Substitute the values back into the expression: Once we have the values of sin(10π/180), sin(250π/180), and sin(310π/180), we can substitute them back into the expression:
- (3sin(10π/180) - 4sin^3(10π/180)) (3sin(250π/180) - 4sin^3(250π/180)) (3sin(310π/180) - 4sin^3(310π/180))

6. Calculate the final result: Evaluate the expression using the calculated values of sin(10π/180), sin(250π/180), and sin(310π/180). This will give us the solution to the original expression.

By following these steps, we can solve the expression **sin^3 10 sin^3 250 sin^3 310** in detail.

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