Question 1046316
3sin^2 theta = 3 - 3 cos^2 theta = 4 cos theta - 1
or
cos^2 theta + 4/3 cos theta - 4/3 = 0

cos theta = 1/2[-4/3 +- sqrt(16/9 + 16*3/3*3)]
cos theta =  -4/6 + 1/2 4/3 sqrt 5
cos theta = 2/3(sqrt(5) - 1)

Can you check?