Google Sheets - Sum values based on date range - filter

I have a column of dates, column C, and a column of values, column G. I want to be able to calculate monthly totals of column G. I've poked around and found that you can use sumif or you can use a filter. The filter method seems easier. I've tried the following but it doesn't work.
=sum(filter(C3:C365,G3:G365>date(3/1/2016),G3:G365<date(3/31/2016)))
How can I check the dates in column C and then sum up the values from column G?
Thanks Rich

Try:
=sumproduct(MONTH(C2:C) = 3,B2:B)
Three is the month number (March).

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It seems like you want to have the difference calculated between two members of the same date field.
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