But stellar abberation contain wrong assumption.
Stellar aberration itself didn't. The ballistic and aether models that tried to explain it did.
Under both of those models, the speed of light needed to be greater.
You may said that we cannot use pythagorean rule in special relativity, maybe something like Einstein velocity addition is needed. But how can we determining angle alpha (the angle at which the telescope must be tilted) if not using pythagorean rule.
You don't use Pythagoras to determine the angle at all.
But there are 3 main ways. One is to determine it all in the reference frame where Earth is moving.
This works quite similar to the diagram above, but the hypotenuse is not the path light is taking.
Light is travelling straight down while the telescope moves to the side.
You use basically the same approach as your triangle, but as I said, light doesn't go down the hypotenuse so it isn't travelling faster than c.
The angle alpha is the inverse tan of the velocity of Earth divided by the speed of light.
You can then either note that the velocity of Earth is quite small and thus approximate the angle for an observer on Earth to be the same, or you can use more complex formulas to transfer between the frames.
Another is to consider it in the reference frame of Earth, noting that the light must be travelling at a velocity of c, and then using the velocity of the reference frame relative to Earth to determine the angle, meaning we use inverse sin instead of inverse tan.
The other option is to use the proper relativistic formulas for relative velocities to find the velocity of the light (in 2D for this case, 3D in more general cases), relative to the observer on Earth (noting that as Earth is moving with a velocity of v in one direction relative to the frame, the frame is moving with a velocity of -v relative to the Earth, although that shouldn't cause any issues).
The horizontal component is easy. It just uses the commonly used formula for relativistic speeds:
(0+v)/(1+0*v/c^2)=v.
So the horizontal component of the velocity of light relative to Earth will be v.
Up next is the vertical component. This is more complex.
Instead of the normal:
(u+v)/(1+u*v/c^2)
you instead have:
sqrt(1-v^2/c^2)*u_v/(1+v*u_h/c^2).
So sticking in the values for our system you get:
sqrt(1-v^2/c^2)*c/(1+v*0/c^2)
=sqrt(c^2-v^2)
Rather than figuring out this directly, it is easier to figure out what the speed will be along the hypotenuse, i.e. the speed along the direction light is travelling)
That will be the square-root of the sum of squares, i.e.:
u=sqrt(v^2+(sqrt(c^2-v^2))^2.
u=c.
And then like before we use inverse sine.
Note that this works out exactly the same as before.
So the options:
Using sine we get an angle of 20.64076007".
Using tan we get 20.64075997"
So basically the same.
But importantly, with the proper relativistic approach, the speed of light remains c in any inertial reference frame.
Increasing the speed of Earth will not make light travel faster relative to Earth.
So aberration isn't a problem for relativity.
How speed stay constant when direction changing, whereas direction determined by pythagorean rule.
Direction is determined from the component velocities, as is speed, but in different ways.
The speed is done by Pythagoras, but the direction is done by trig.
The component velocities change, and thus the direction does, but the overall speed remains the same.