Tính giá trị biểu thức

$\text{cos²$\dfrac{π}{7}$ + cos²$\dfrac{2π}{7}$ + cos²$\dfrac{3π}{7}$}$
$\text{= $\dfrac{1}{2}$(1 + cos$\dfrac{2π}{7}$) + $\dfrac{1}{2}$(1 + cos$\dfrac{4π}{7}$) + $\dfrac{1}{2}$(1 + cos$\dfrac{6π}{7}$)}$
$\text{= $\dfrac{1}{2}$(1 + cos$\dfrac{2π}{7}$ + 1 + cos$\dfrac{4π}{7}$ + 1 + cos$\dfrac{6π}{7}$)}$
$\text{= $\dfrac{1}{2}$(3 + cos$\dfrac{2π}{7}$ + cos$\dfrac{4π}{7}$ + cos$\dfrac{6π}{7}$)}$
$\text{= $\dfrac{3}{2}$ + $\dfrac{1}{2}$(cos$\dfrac{2π}{7}$ + cos$\dfrac{4π}{7}$ + cos$\dfrac{6π}{7}$)}$
$\text{= $\dfrac{3}{2}$ + $\dfrac{1}{4sin\dfrac{π}{7}}$(2sin$\dfrac{π}{7}$cos$\dfrac{2π}{7}$ + 2sin$\dfrac{π}{7}$cos$\dfrac{4π}{7}$ + 2sin$\dfrac{π}{7}$cos$\dfrac{6π}{7}$)}$
$\text{= $\dfrac{3}{2}$ + $\dfrac{1}{4sin\dfrac{π}{7}}$(sin$\dfrac{3π}{7}$ - sin$\dfrac{π}{7}$ + sin$\dfrac{5π}{7}$ - sin$\dfrac{3π}{7}$ + sin$\dfrac{7π}{7}$ - sin$\dfrac{5π}{7}$) }$

$\text{= $\dfrac{3}{2}$ + $\dfrac{1}{4sin\dfrac{\pi}{7}}$(- sin$\dfrac{π}{7}$ + 0)}$

$\text{= $\dfrac{3}{2}$ + $\dfrac{-1}{4}$ }$

$\text{= $\dfrac{5}{4}$}$

$\textit{@Ha1zzz}$

$\textit{#Overthinker?}$