Using `FindAllCrossings` from [here][1],

 FindAllCrossings[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, -10, 10}, 
 WorkingPrecision -> 20]

> {-4.9295434376879868373, -3.7745180124835511931, 0.76290087955924483126, 3.3574487606850113852}


 [1]: https://mathematica.stackexchange.com/questions/5663/about-multi-root-search-in-mathematica-for-transcendental-equations/5666#5666