A chord of a circle subtends an angle of θ at the centre of the circle.

We know that the area of circle and area of minor segment of angle $\theta$ in a circle of radius $r$ is given by, $A^{\prime}=\pi r^{2}$ and $A=\left\{\frac{\pi \theta}{360^{\circ}}-\sin \frac{\theta}{2} \cos \frac{\theta}{2}\right\} r^{2}$ respectively.

It is given that,

Area of minor segment $=\frac{1}{8} \times$ area of circle

$\left\{\frac{\pi \theta}{360^{\circ}}-\sin \frac{\theta}{2} \cos \frac{\theta}{2}\right\} r^{2}=\frac{\pi r^{2}}{8}$

$\left\{\frac{\pi \theta}{360^{\circ}}-\sin \frac{\theta}{2} \cos \frac{\theta}{2}\right\} \times 8=\pi$

$\frac{8 \pi \theta}{360^{\circ}}-8 \sin \frac{\theta}{2} \cos \frac{\theta}{2}=\pi$

$\frac{\pi \theta}{45^{\circ}}-8 \sin \frac{\theta}{2} \cos \frac{\theta}{2}=\pi$

$\frac{\pi \theta}{45^{\circ}}=8 \sin \frac{\theta}{2} \cos \frac{\theta}{2}+\pi$