The sector $OAB$ contains the triangle $OAB$ and the minor segment $AB.$

1. Given that the area of the triangle is equal to the area of the segment, show that

   $$\frac{\theta }{2}=\sin \theta$$

2. Hence, use iteration with a starting value of ${\theta }_0=\frac{\pi }{2}$ to find three further approximate values, ${\theta }_1,{\theta }_2,{\theta }_3$ for $\theta .$

You need to multiply by two first, and use the iterative formula

Give the value of ${\theta }_3$ to $3$ significant figures.