Prove that `sinx+2xgeq(3x(x+1))/pi, AA x in [0,pi/2]` (Justify the inequality, if any used).

Explanation

To prove that \( \sin x + 2x \geq \frac{3x(x + 1)}{\pi} \) for all \( x \in [0, \frac{\pi}{2}] \), we will define a function and analyze it step by step.

### Step 1: Define the function
Let us define the function:
\[ f(x) = \sin x + 2x - \frac{3x(x + 1)}{\pi} \]
We need to show that \( f(x) \geq 0 \) for \( x \in [0, \frac{\pi}{2}] \).
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