The Daily Move That Pays the Theta

You buy an at-the-money call on a stock trading at $\$100$ with $30$ trading days to expiry, paying an implied volatility of $32\%$, and you delta-hedge it once at the end of each trading day. Work throughout in trading time: a year is $256$ trading days, so the option's life is $T = 30/256$ years. Ignore interest rates and dividends.

(a) How large does the stock's daily move have to be, in dollars and in percent, for the position to break even on the day? (b) The stock in fact moves about $1.2\%$ per day, in a random direction. Do you make or lose money, and how would you describe the trade in one sentence to a risk manager? (c) The option's gamma is $0.0364$ per share. What is its theta per trading day?