A point source $($Tc$-99$m$,140$ keV gamma emission$)$ is located at the center. Five pinholes are shown in the right figure. The distances between the side pinholes to the center pinhole are all equal. Pinhole insert and shield are made of lead $($ Pb $).$ The circular pinhole aperture size is $0\mathrm{.}3$ cm $($diameter$).$ is $30.a$ is $30.$ Density of Pb is $11\mathrm{.}34\frac{g}{c}{m}^3.$ Mass attenuation coefficient of Pb is $2\mathrm{.}390\frac{c{m}^2}{g}$ at this energy $(140$ keV $).t=15cm,b=20cm.$

Calculate the total geometric efficiency of all five pinholes combined in a fraction $($not in $\%).($Write at least three significant numbers in your answer.$)$

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