Good luck!
My policy for figuring sun angles is amateur-hour, not computation-intensive. I wait for the relevant season to roll around, then look at the shadows, morning noon and evening. If I want to make a window "more sunny in winter" or "shadier during summer afternoons", I look and think in the relevant season. (I don;t visualize geometry or angles easily.)
The winter sun might not get very high in the sky, even at noon, but I think winter is when the east-and-west sun angle becomes broader (the sun rises farther to the east and sets farther to the west in winter than in summer - or do I have that backwards?)
But I don't think you'll go too far wrong removing trees or big branches that are south of your new bed (unless you fear a fierce noon-time sun).
Removing trees (or low branches or even bushes) that are south-east of your bed should give you more (low) morning sun. I think that would be a big advantage for a cold-frame or a sheltered hardening-off bed, or early-early spring crops like peas.
Removing trees (or low branches or even bushes) that are south-west of your bed should give you more (low) late-afternoon sun. That should be helpful to heat-loves like tomatoes, peppers or eggplant.
LEAVING some afternoon shade might be good for a bed full of cool-weather late-spring crops, extending their season into late spring or summer, depending on how hot your early summers get.
Personally, I dread tree roots as much as I dread shade. If you have three whole acres, maybe appreciate the trees in two of those acres, with footpaths or even a chair or bench, but appreciate full-sun-veggy-beds in the acre nearest the house!
