I just don't understand the geometry behind this! How is theta 1 in red equal to theta 1 in black? And same with theta 2? I need to figure out the angles to solve the rest of my problem, but I am already stuck in figuring out how these angles are the same. Please help asap.

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  1. Looks like they are doing some kind of rotation.

    Here is an easier way:

    from red B1 draw a perpendicular to the x-axis to get a right-angled triangle.
    So the angle at red B1 is black Ø2

    since in the original Ø1+Ø2=90
    and in the new triangle the angle at P must be Ø1

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