Hedged P&L of a short straddle

A trader sells one lot of the Nifty Dec 24,700 straddle (call plus put) at an implied volatility of 12.5% and delta-hedges with Nifty futures. (a) Derive the approximation $d\Pi\approx\tfrac12\Gamma S^2[(dS/S)^2-\sigma^2dt]$ for a delta-hedged long option position financed at $r$, starting from Itô's lemma and the PDE. (b) Compute the straddle's per-lot gamma and theta (per calendar day) with the notes' inputs ($q=0.491\%$). (c) Estimate the hedged P&L of the short straddle per lot over one calendar day if Nifty moves 1.5%; if it moves 0.5%. Find the breakeven daily move. (d) What does the answer imply about the risk of short-premium strategies, and why is the approximation worse for a 3% gap than for a 1.5% move?