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Some interesting facts behind the De Moivres Theorem with the light of Geometrifying Trigonometry(C) is that we have now special arrangements of different symmetric settings of multiplications and divisions which are both the * operations where division reverses the duplets of GT_Query_Strings(C) and continue with same kind of Align Scale To Fit systems where we see that ∞(ALT+236) type of fundamental multiplication operator will always expand the systems of Geometrifying Trigonometry NARRAYS(C) [N ARRAY ARRANGEMENTS OF ALIGNED SHAPES OF Geometrifying Trigonometry(C) LOCKED SETS(C)] where from the observations on Debashis Bhunias AUTOLISP outputs for the Sanjoy Nath's Geometrifying Trigonometry(C) Algorithms on Locked Sets(C) we can see that there are some expanding of shapes outlines nature present in ∞(ALT + 236) operations on Sin(Θ) and on Cos(Θ) .We call that as SinSpansion or CosSpansion , and the cases of ∞ operations on Sec(Θ) we call that SecSpansions . Similarly there are cases of TanSpansions , CosecSpansions , CotSpansions . Normally we have never seen any kind of contraction due to Union Outline Operation on GeometrifyingTrigonometry(C) Narays(C) but keeping intact in size of outlines with that of Seed Triangle [SEED_TRIANGLE(C) is the smallest possible basis LOCKED_SET(C) of GeometrifyingTrigonometry(C)] is the invariant nature of NARRAYS_OUTLINES(C) [We need to check for INTERSECTION_OF_NARRAYS(C) called NARRAYS_INLINES(C)] which are Contractions of Narrays(C) instead of Expansions of Narays due to merging. These are called as SinTraction , CosTraction,TanTraction,CosecTraction,SecTraction,CotTraction. We have several kinds of theorems on Geometrifying Trigonometry Operator Arithmatics where only expansions are possible and some of the operators sequences have very interesting properties of contraction of NARRAYS(C) merging which we will study in different theorems of Geometrifying Trigonometry.Very interesting natures of overlaps and the merging orientations exposes several insights hidden inside De Moivres Theorem which was vanished due to over usages of complex numbers.Complex number is a very useful tool in Current mathematics which was once called DOUBLE ALGEBRA due to DE MORGAN , has taken a large space of mathematics but that hides many of possible geometric interpretations and hides secrets inside its invisible ARGAND PLANE. Sanjoy Nath's Geometrifying Trigonometry(C) is exposing these hidden arrangements on 2D Euclidean Plane through the insertion of concept of LOCKED_SET(C) and through the very new operation called ALIGN_AND_SCALE_TO_FIT with four different possible symmetric arrangements which are very natural to common sense without any doubt.The big geometry giant Autodesk has even understood the importance of this operation long time back.This operation came to dilemma when Sanjoy Nath's Geometrifying Trigonometry(C) appeared with all possible forms of symmetric arrangements possible due to ALIGN_AND_SCALE_TO_FIT operation redefined with MINIMUM_ENERGY_ROTATION_WHILE_PIVOTING ∞ (ALT + 236) and consecuitive three other 3 operations (ó , ö , ô(not taken here) , ò) of mirroring about symmetric axis of merged line revamped the GEOMETRIZATION or GEOMETRIFICATIONS of many hidden REAL PICTURES on 2D REAL EUCLIDEAN PLANE which were hidden inside ARGAND PLANES for many years.Lets see the playground of these Theorems on SinCpansions , CosSpansions , TanSpansions , CosecSpansions , SecSpansions , CotSpansions , SinTractions , CosTractions , TanTractions , CosecTractions , SecTractions , CotTractions in System Theory , Chaos Theory , through the study of dynamics of arrangements of different line segments in Geometrifying Trigonometry(C) systems of Picture framework on Trigonometric Objects.