@_Maxim_ Thank you for your help

@_Maxim_ how I can obtain results in table or array form?

@_Maxim_ I got your code but how I can specific value at specific point?

Many thanks for your contiuose support

@_Maxim_ thanks alots for your help

these equations represent an ellipse passing in three points and tangent at one of them

there is only one unique solution at each angle x5

many thanks for your help

can you help me how you assume that x5=2Pi/5?