$${Find}\:\:{a}\:\:,\:\:{if}\:\:\left[\:{yellow}\:\right]\:=\:\:\left[\:{blue}\:\right] \\$$$${Area}\:\:{of}\:\:{yellow}\:\:=\:\:{area}\:\:{of}\:\:{blue} \\$$
$${let}\:{R}=\mathrm{1} \\$$$$\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}\left[\frac{\pi}{\mathrm{2}}+\mathrm{2}{a}−\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}+\mathrm{2}{a}\right)\right]−\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}−\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right)−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}×\sqrt{\mathrm{2}}\:\mathrm{tan}\:{a}=\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}−\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right) \\$$$$\Rightarrow\mathrm{2}{a}−\mathrm{cos}\:\mathrm{2}{a}−\mathrm{2}\:\mathrm{tan}\:{a}=\frac{\pi}{\mathrm{4}}−\frac{\mathrm{3}}{\mathrm{2}} \\$$$$\Rightarrow\mathrm{cos}^{\mathrm{2}} {a}+\mathrm{tan}\:{a}−{a}=\frac{\mathrm{10}−\pi}{\mathrm{8}} \\$$$$\Rightarrow{a}\approx\mathrm{0}.\mathrm{4255}=\mathrm{24}.\mathrm{38}° \\$$