Solve "Circles and Sectors: 3θ=2(π−sinθ)

[look416]

Homework Statement

The diagram shows a semicircle APB on AB as diameter. The midpoint of AB is O. The point P on the semicircle is such that the area of the sector POB is equal to twice the area of the shade segment. Given that angle POB is \theta radians, show that

3\theta = 2(\pi-sin\theta)​

Homework Equations

The Attempt at a Solution

using formula
Area of circle = \frac{1}{2}r²\theta
and
Area of segment = \frac{1}{2}r² (\theta - sin \theta )
heres the problems
from the picture http://img130.imageshack.us/img130/1790/001tz.jpg
questions 4
the the angle of the segment is \pi-\theta
there I am clueless even i inserted the info i have
what i really get is

\theta=2[\pi-\theta-sin(\pi-\theta)]​

of course we can't use formula blindly so anyone can help me there

 

[rock.freak667]

If sector POA contains the shaded segment and triangle POA, how do you find the area of the shaded region?