MHB Trigonometric of tangent and sine functions

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Simplify $\left(\tan \dfrac{2\pi}{7}-4\sin \dfrac{\pi}{7}\right)\left(\tan \dfrac{3\pi}{7}-4\sin \dfrac{2\pi}{7}\right)\left(\tan \dfrac{6\pi}{7}-4\sin \dfrac{3\pi}{7}\right)$.
 
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I got about -8.7083121069873265814843145114959219999438416220762493062309701968483080116471438626714199913273209202440106287205185869613863265722279384849632901398226721432702744787955199077781973792055631357781755415456733331388124469116498805756011983384506433640247288593850820089590928253650738597742412754348439402301589178427587352708579714081417809559865987679591010005488147679340458470850085945675037017144904042287279335497160556553452963874716319026939725908000014025345344112227718546669183167834689374961602264946845122520973969612465747159538537772604016219227651262298967156522926816165972425283143645081705710618441263404832174787619393871431981552587401078586609898568054592224581007986448669288148444215128498186229896741206349315952054866256984612864167199842472866575465952447085845790874114020207148838309575537421068097653460699858226519033408205869208586639796284569971790165922274544500088737294024496093237634962135759638417523292668843921768916664652250085254395250841082981914897137469833874653795905403859395226103590166597307639852476273392879083873723649605334228340639098097814440444549718831560592044450598723461692804007733588937741590648889021935199757480637837660523461803937847078950866107512314217003731198786042996011750451712135884514444878781114357178952544416819768594073353584110967734337432198244086867356343864416552649586451520413569547092694404444532795994994438271445333716459116502792251091594744077024600155160457563503684373664211499889132746530159707148096441069149624420565803877227318131627873671715105932608979648146278844613590157353436714676787933231516958800501704045205913556958442328349254532043183475963879427381686337157339601066369199608533673687386762949721994907024739645071023865884051877078161059364899178505753714909479228031574944638783941268199880771092085126999780242627307210910698666574484989827761671955524479251591513340499083326461726929118742316319408632872884749801756534634165971359295929387392681708974873301182019170001880197471302122860499952496977...

Am I close?

-Dan
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
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Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
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Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
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