If cos (α - Π / 6) + sin α = (4 / 5) √ 3 is known, then what is the value of sin (α + 7 Π / 6)?

If cos (α - Π / 6) + sin α = (4 / 5) √ 3 is known, then what is the value of sin (α + 7 Π / 6)?

The expansion of COS (α - Π / 6) + sin α = 4 √ 3 / 5 gives 1 / 2cos α + √ 3 / 2Sin α = 4 / 5
Then the auxiliary angle formula is used to get sin (α + π / 6) = 4 / 5
sin(α-7∏/6)=cos(α+π/6)
According to the square relation of the same angle, sin (α - 7 Π / 6) = 3 / 5 or - 3 / 5