What is the general solution for 4sin^2(x-pi/3)=3 ?

The general solution for 4sin^2(x-pi/3)=3 is x=(2pi)/3+2pin,x=2pin+pi,x=2pin+(5pi)/3 ,x=2pin+2pi

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4sin^2(x-pi/3)=3

4 sin^{2} (x - \frac{π}{3}) = 3

x = \frac{2 π}{3} + 2 πn, x = 2 πn + π, x = 2 πn + \frac{5 π}{3}, x = 2 πn + 2 π

Solution steps

4 sin^{2} (x - \frac{π}{3}) = 3

Solve by substitution

sin (x - \frac{π}{3}) = \frac{3}{2}, sin (x - \frac{π}{3}) = - \frac{3}{2}

sin (x - \frac{π}{3}) = \frac{3}{2} : x = \frac{2 π}{3} + 2 πn, x = 2 πn + π

sin (x - \frac{π}{3}) = - \frac{3}{2} : x = 2 πn + \frac{5 π}{3}, x = 2 πn + 2 π

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = 2 πn + π, x = 2 πn + \frac{5 π}{3}, x = 2 πn + 2 π

cos (θ) = - 0.89

cos (θ) = - 0.81

cos (θ) = - 0.44

cos (θ) = - 0.62

2 - 2 sin^{2} (x) = 2 cos^{2} (\frac{x}{2})

What is the general solution for 4sin^2(x-pi/3)=3 ?
The general solution for 4sin^2(x-pi/3)=3 is x=(2pi)/3+2pin,x=2pin+pi,x=2pin+(5pi)/3 ,x=2pin+2pi