<prompt> Acha alpha,beta, na gamma ziwe pembe tatu ili alpha beta gamma pi. Tukipewa hiyo tan alpha tan beta csc fracpi3, kisha ubaini fraccos alpha cos betacos gamma.  <response>: Kwanza, tan alpha tan beta csc fracpi3 frac2sqrt3. Kishasin alpha sin beta frac2sqrt3 cos alpha cos beta.Sasa, kutoka kwa fomula ya kuongeza pembe,anzaaligncos gamma cos pi - alpha - beta -cos alpha beta dhambi alpha sin beta - cos alpha cos beta frac2sqrt3 cos alpha cos beta - cos alpha cos beta frac2 - sqrt3sqrt3 cos alpha cos beta.mwishoalignKwa hiyo,fraccos alpha cos betacos gamma fracsqrt32 - sqrt3 fracsqrt3 2 sqrt32 - sqrt32 sqrt3 2 sqrt3 3. 