Zestt

The corporation is taxed 30% on earnings paid as dividends, leaving 70% to be paid to the shareholders.  The shareholders pay 40% taxes on the dividends, leaving them with 60% of the dividends paid.  Thus, the shareholders end up with 42% (= 60% of 70%) of the earnings paid as dividends.  If they end up with 42% of the earnings paid as dividends, the taxes paid amount to 58% of the earnings paid as dividends.
If you want a simple formula (I wouldn’t bother, personally), it’s:
1 – (1 – tc)(1 – ti) = 1 – (1 – tc – ti + tc