calculus - Use the mean value theorem to prove that

Use the Mean Value Theorem to prove that

$$\frac{\pi}{6} + \frac{(2x-1)}{\sqrt3} < \arcsin x < \frac{\pi}{6} + \frac{(2x-1)}{2\sqrt{1-x^2}} \qquad \text{for} \ \frac{1}{2}\leq x< 1.$$

How can I prove the inequality above?
Give me a clue or a full proof.