$ =2 \pi(1-\cos \theta)$

$=2 \pi\left(1-\cos 45^{\circ}\right)$

$=2 \pi\left(1-\frac{1}{\sqrt{2}}\right)$

Flux entering through curved surface $=$ flux leaving through flat surface

$\Rightarrow$ Flux entering through curved surface $=-\frac{\mathrm{Q}}{\varepsilon_0} \times \frac{1}{4 \pi} \times 2 \pi\left(1-\frac{1}{\sqrt{2}}\right)$

$=-\frac{Q}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$

Also all points of circumference are at equal distance from the charge