/ / ___________\ / ___________\ \
| | / ___ | | / ___ | |
| |\/ 2 + \/ 2 | |\/ 2 - \/ 2 | |
And|x < pi - atan|--------------|, atan|--------------| < x|
| | ___________| | ___________| |
| | / ___ | | / ___ | |
\ \\/ 2 - \/ 2 / \\/ 2 + \/ 2 / /
$$x < \pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)} \wedge \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)} < x$$
(atan(sqrt(2 - sqrt(2))/sqrt(2 + sqrt(2))) < x)∧(x < pi - atan(sqrt(2 + sqrt(2))/sqrt(2 - sqrt(2))))
/ ___________\ / ___________\
| / ___ | | / ___ |
|\/ 2 - \/ 2 | |\/ 2 + \/ 2 |
(atan|--------------|, pi - atan|--------------|)
| ___________| | ___________|
| / ___ | | / ___ |
\\/ 2 + \/ 2 / \\/ 2 - \/ 2 /
$$x\ in\ \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}, \pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)}\right)$$
x in Interval.open(atan(sqrt(2 - sqrt(2))/sqrt(sqrt(2) + 2)), pi - atan(sqrt(sqrt(2) + 2)/sqrt(2 - sqrt(2))))