into confidence

“Government should take the local people into confidence before the start of the project.”
Is this sentence correct?
Can it be rephrased to look better?

“Government should take the local people into their* confidence before the start of the project.”

*Or “its”, depending on preference.

Dozy,
Can I say?:
“Government should take the local people into its confidence before starting of the project.”"

‘… before starting of the project’ is incorrect.

If you are talking about one particular government, rather than government in general, you also require a definite article in each of the above sentences:

The government should take…

If you are speaking about a number of governmental bodies rather than government in general you would require the plural ‘governments’.