Finding some complicated enclosed region in polar coordinates

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In polar graphing system, I know how to find areas of simple regions, or even simple enclosed regions by two given polar equations, however for more overlapped regions when we have multiple graphs for instance when I tried to graph this flower using these equations:

$r=3.4 \cos⁡(4θ-5)$

$r=3.4 \cos⁡(4θ+5)$

$r=3.4 \cos⁡(4θ)$

enter image description here Like when I graph this on desmos or some polar graphing software we have so many overlaps. So how can one mathematically find the area of this entire region enclosed by these three polar curves properly $?$