**Note: This is just to show how to get the number of days.**

Here's how i set it up, so feel free to change it once you understand how it works. I set it up by putting the number of days from C1-C12 with D2 being a leap year (feel free to change the code to reflect numbers instead of cells)

A1 = start date
A2 = `MONTH(A1)`

A2 = `MONTH(A1)+1`

A3 = `MONTH(A1)+2`

B1 = `=A1+B5`

B2 = `=IF(A2=1,C1,IF(A2=2,IF((MOD(YEAR(A1),4))=0,D2,C2),IF(A2=3,C3,IF(A2=4,C4,IF(A2=5,C5,IF(A2=6,C6,IF(A2=7,C7,IF(A2=8,C8,IF(A2=9,C9,IF(A2=10,C10,IF(A2=11,C11,IF(A2=12,C12,0))))))))))))`

B3 = `=IF(A3=1,C1,IF(A3=2,IF((MOD(YEAR(A1),4))=0,D2,C2),IF(A3=3,C3,IF(A3=4,C4,IF(A3=5,C5,IF(A3=6,C6,IF(A3=7,C7,IF(A3=8,C8,IF(A3=9,C9,IF(A3=10,C10,IF(A3=11,C11,IF(A3=12,C12,0))))))))))))`

B4 = `=IF(A4=1,C1,IF(A4=2,IF((MOD(YEAR(A1),4))=0,D2,C2),IF(A4=3,C3,IF(A4=4,C4,IF(A4=5,C5,IF(A4=6,C6,IF(A4=7,C7,IF(A4=8,C8,IF(A4=9,C9,IF(A4=10,C10,IF(A4=11,C11,IF(A4=12,C12,0))))))))))))`

B5 = `=SUM(B2,B3,B4)`

This is just the long way around, but my point of doing this is for B5, this will give you the number of days between each month, but really the day of the month is always going to be the same. I threw B1 in there just to show that as well, but you need to set all cells to be general or a number, and A1 and B1 are dates for the cell type.

A2-4 are the 3 months, B2-4 are the number of days in those months, and B5 is the total number of days. This includes a leap year, but if you just want a straight 3 months after, use the answer user1016274 gave you.

Have fun! :)