hello,
can you give some hints to prove the following:
|1-exp(i theta)|>=2|theta|/pi whenever -pi<=theta<=pi

2. i had read some latex tutors on this forum and this is the inequality above:

$\forall -\pi\leq\theta\leq\pi : |1-\exp(i \theta)|\geq \frac{2 |\theta|}{\pi}$

3. Recall Euler's formula:

$e^{i\theta}=cos(\theta)+isin(\theta)$

And:
$|1- cos(\theta)-isin(\theta)|= (1-cos(\theta))^2+sin^2(\theta)$

4. ok, i could arrive at:
$|1-e^{i\theta}|=2|sin(\frac{\theta}{2})|$

but how can i extract the term $\frac{\theta}{\pi}$ from the above equation?

5. hello,
please any ideas to solve the above problem?