Angle/Orient/Direction in Saints Row 2

The Angle/Orient/Direction system in Saints Row 2's cts files work like these:
  • 0.00: South
  • 1.55: West
  • 3.15: North
  • 4.70: East
  • Angle value loops to South around ~6.29
I haven't checked thoughtfully yet, but if the angle value is negative, the angle probably moves in counterclockwise.

Here is a rough diagram of angles observed from the game:
angles.png


I've also created a custom mission "Angle Checker" for SuperUI which warps you to <0,0,0> coordinate and lets you to change angles by pressing E or R keys.
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What do store takeover cam Orient numbers stand for?
In the square brackets containing 3 pairs of the arrow brackets?
 
What do store takeover cam Orient numbers stand for?
In the square brackets containing 3 pairs of the arrow brackets?
Haven't really messed with this, but my personal guess is that these are "waypoints" of camera rotation during "Store Purchased" screen.
 
I found the northern Barrio sloppy seconds camera has almost the right angle I want (but still a bit pointing north east)

Code:
looking towards the shop as I would like
$Navpoint:    "shops_sr2_city_$BAR_slop_cam1"
$Type:        "floating"
$Pos:            <211.272858 -1.689102 605.426697>
$Orient:        [<-0.862195 0 0.506576> <-0.041565 0.996628 -0.070744> <-0.504868 -0.082051 -0.859288>]

$Navpoint:    "shops_sr2_city_$BAR_slop_cam2"
$Type:        "floating"
$Pos:            <219.378922 1.471883 615.440674>
$Orient:        [<-0.824322 0 0.566121> <-0.021860 0.999254 -0.031831> <-0.565699 -0.038615 -0.823708>]

while the Arena rim jobs is probably the same or in similar direction
$Navpoint:    "shops_sr2_city_$AR_rim_cam1"
$Type:        "floating"
$Pos:            <840.801819 -1.692311 -187.506775>
$Orient:        [<-0.942979 0 0.332851> <-0.042246 0.991913 -0.119685> <-0.330159 -0.126922 -0.935353>]

$Navpoint:    "shops_sr2_city_$AR_rim_cam2"
$Type:        "floating"
$Pos:            <840.818054 3.855494 -177.225586>
$Orient:        [<-0.928639 0 0.370985> <-0.043165 0.993208 -0.108048> <-0.368465 -0.116351 -0.922332>]

Somehow I got the camera look to the vague south while panning out
$Navpoint:    "shops_sr2_city_$AR_volition_cam1"
$Type:        "floating"
$Pos:            <835.600000 -2.2 -324.500000>
$Orient:        [<0.98480 0 0.17364> <0 0 0> <-0.17364 0 0.98480>]

$Navpoint:    "shops_sr2_city_$AR_volition_cam2"
$Type:        "floating"
$Pos:            <830.000000 3.1 -304.500000>
$Orient:        [<0.98480 0 0.17364> <0 -0.5 0> <-0.17364 0 0.98480>]
Hopefully something can be found out
 
Excuse me, can you improve the Orient Check task so that the protagonist can check the angle in any place instead of just one place?
 
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