What is the general solution for -5/2 csc(θ/2)=-sqrt(3)-csc(θ/2) ?

The general solution for -5/2 csc(θ/2)=-sqrt(3)-csc(θ/2) is θ=(2pi)/3+4pin,θ=(4pi)/3+4pin

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-5/2 csc(θ/2)=-sqrt(3)-csc(θ/2)

- \frac{5}{2} csc (\frac{θ}{2}) = - 3 - csc (\frac{θ}{2})

θ = \frac{2 π}{3} + 4 πn, θ = \frac{4 π}{3} + 4 πn

Solution steps

- \frac{5}{2} csc (\frac{θ}{2}) = - 3 - csc (\frac{θ}{2})

Solve by substitution

csc (\frac{θ}{2}) = \frac{2 3}{3}

csc (\frac{θ}{2}) = \frac{2 3}{3} : θ = \frac{2 π}{3} + 4 πn, θ = \frac{4 π}{3} + 4 πn

Combine all the solutions

θ = \frac{2 π}{3} + 4 πn, θ = \frac{4 π}{3} + 4 πn

4 cos (2 θ) + 11 sin (θ) - 4 = 3

sinh (x) = \frac{7}{24}

cos (x) = \frac{5}{15}

cos (θ) = \frac{3}{5}, 0 < θ < \frac{π}{2}

sin (x) - cos^{2} (x) sin (x) = - 1

What is the general solution for -5/2 csc(θ/2)=-sqrt(3)-csc(θ/2) ?
The general solution for -5/2 csc(θ/2)=-sqrt(3)-csc(θ/2) is θ=(2pi)/3+4pin,θ=(4pi)/3+4pin