If $sin alpha + sin beta + sin gamma = cos alpha + cos beta + cos gamma$ then what is the value of $cos^2 alpha + cos^2 beta + cos^2 gamma$ ?

The question gives insufficient information to determine a unique value.

For example:

If $(alpha, beta, gamma) = (0, pi, pi/4)$ then:

${ (sin alpha + sin beta + sin gamma = 0+0+sqrt(2)/2 = sqrt(2)/2), (cos alpha + cos beta + cos gamma = 1-1+sqrt(2)/2 = sqrt(2)/2), (cos^2 alpha+cos^2beta+cos^2gamma = 1+1+1/2 = 5/2) :}$

If $(alpha, beta, gamma) = (pi/4, pi/4, pi/4)$ then:

${ (sin alpha + sin beta + sin gamma = sqrt(2)/2+sqrt(2)/2+sqrt(2)/2 = (3sqrt(2))/2), (cos alpha + cos beta + cos gamma = sqrt(2)/2+sqrt(2)/2+sqrt(2)/2 = (3sqrt(2))/2), (cos^2 alpha+cos^2 beta + cos^2 gamma = 1/2+1/2+1/2 = 3/2) :}$

Are $alpha, beta, gamma$ supposed to be the internal angles of a triangle or something like that? Is there some information missing from the question?