What is the climb-out angle of a twinjet upon one engine failure scenario?
The 737 and A320 are certified under Part 25, and they meet the certification requirement in 14 CFR § 25.121. With the gear retracted and one engine out:

... The steady gradient of climb may not be less than 2.4 percent for two-engine airplanes ...

Aircraft Flight Manuals (AFMs) don't typically include the all-engines gradients of climb as noted in AC 120-91A:

... It is recognized that many AFMs generally contain only the OEI performance for loss of an engine at V$_1$ on takeoff ... [emphasis added]

The OEI (One-Engine Inoperative) scenario is what matters more for obstacle clearance.
MTOW alone isn't useful
The performance tables are typically set up for ease of use. Instead of gradients, they list the maximum weights that would guarantee the regulatory gradient for the different pressure altitudes and temperatures, which are known as climb limit weights.
Consider a 737-800 at MTOW at a hot-and-high airport, it is not given that it can attain the 2.4% with an engine out. The TOW needs to respect the climb limit.
And a 737-800 at MTOW at sea level and cold temperature may exceed the 2.4% with an engine out. In this case, that 737 is not climb limited.

As an example, here's the climb limit graph for a 737-800 with flaps 5, note how when it's hotter and/or higher, the climb limit weight is reduced.


Source: 737-800 FPPM; click to view