This is going to be a matter of negotiation between you. You have no legal right to buy her out, unless you entered into an agreement to that effect at the outset when you gave away the 40% of the shareholding.
If you cannot reach agreement on buying her out, then you would have to to continue with her existing as a shareholder, or seek to wind up the company.
If you do have to wind up the company, then you could always start a new company afterwards, without her involvement.
As to the appropriate figure, it is a matter of discussion and negotiation, but it is often helpful to have an expert valuer place to value on the company, so the shares can be properly valued.
Yes, it can often be difficult in these situations to resolve. Nobody ever wants to force the other one out, and there is little scope left after that, other than to apply to the court.
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