Domain: Organic synthesis

An organic compound ethyl 5-nitro-2-vinylpentanoate reacts with 1-chloro-4-isocyanatobenzene in the presence of triethylamine (Et$_3$N) and benzene (PhH) at $25\,^\circ\mathrm{C}$, followed by reaction with H$_2$ and Raney Ni in methanol (MeOH), water (H$_2$O), and acetic acid (AcOH), leading to the formation of organic product A. Thereafter, product A is treated with methanesulfonyl chloride in the presence of triethylamine (Et$_3$N) at $0\,^\circ\mathrm{C}$, resulting in formation of the final organic product.
 Calculate the total number of $\pi$ bonds in the final organic product.

Grading rubric:
criterion: Identifies the ethyl 5-nitro-2-vinylpentanoate as starting material-1 (SM1).
weight: 10
criterion: Identifies Step 1 (Et3N, PhH) explicitly as a 1,3-dipolar cycloaddition between SM1 and 1-chloro-4-isocyanatobenzene.
weight: 10
criterion: States the Step 1 product explicitly as ethyl (3aS,4R)-3a,4,5,6-tetrahydro-3H-cyclopenta[c]isoxazole-4-carboxylate.
weight: 10
criterion: Identifies Step 2 (H2, Raney Nickel, MeOH, H2O, AcOH) as hydrogenolysis of the isoxazole ring.
weight: 20
criterion: States the hydrogenolysis product explicitly as ethyl (1R,2R)-2-(hydroxymethyl)-3-oxocyclopentane-1-carboxylate.
weight: 10
criterion: States the final product explicitly as ethyl (R)-2-methylene-3-oxocyclopentane-1-carboxylate
weight: 20
criterion: Identifies the ester carbonyl group in the final product as contributing exactly one $\pi$ bond.
weight: 10
criterion: Correctly states the total number of $\pi$ bonds present in the final organic product as exactly 3.
weight: 10

Answer:
3 pi bonds