Should all four quarterly tax payments be in equal amounts?

No! The tax billing year begins July 1st, and ends June 30th. The 1st two quarterly bills are issued on or about July 1st and are due and payable in two installments, The 1st installment is due August 1st and the 2nd installment is due November 1st.  The actual tax bill is generally issued as the 3rd quarter bill. The 3rd and 4th quarter installments are issued in one mailing, on or about January 1st, and become due February 1st and May 1st. You should note that the preliminary bills (1st and 2nd quarter) are issued in equal amounts. They each represent 1/4 each of the prior year's total net tax (along with the projected increase factor). Once the tax rate is set in December, and the actual tax amount for the year is known, the 3rd and 4th quarter installments are issued minus the preliminary amounts billed. The 3rd and 4th quarter bills are the result of the difference between the total tax liability for the year minus the preliminary amounts. (valuation x tax rate) – (quarter 1 & 2 payments) = 3rd & 4th quarter bills.