find value of cot 15  degree + cot 75 degree +cot 315 degree

Dear student
Cot150+cot750+cot3150=Cot150+Cot(900-150)+cot(3600-450)=Cot150+tan150-cot450(Applying ASTC rule)=cos150sin150+sin150cos150-1=cos2150+sin2150sin150.cos150-1=1sin150.cos150-1=22.sin150.cos150-1=2sin300-1=212-1=3
Hope this clears your doubt 
With regards 

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