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?