limits of brocard angle

[Tahmid Hasan]

Prove that brocard angles can not be bigger than $30$ degrees.
if you don't know about brocard angles and points then here's 2 links:
en.wikipedia.org/wiki/Brocard_points
http://mathworld.wolfram.com/BrocardPoints.html

[*Mahi*]

Hint:

Use Jensen's inequality-
For $x_i\in [0,\pi]$
$\sum \frac{sin x_i}{n}\leq {sin {\frac{\sum x_i}{n}}}$

[Tahmid Hasan]

hehe,i used Erdos-mordell inequality:
math.ust.hk/excalibur/v2_n4

[*Mahi*]

Yeah,that also works,but Jensen's inequality works in much more cases(I mentioned only a special case)