I really don't understand how to write the expression as one invloving only sinϴ and cosϴ
sin2ϴ+cos3ϴ
first of all you should by now have proven that
sin 2x = 2sinxcosx
by writing cos 3x as cos(2x + x), expanding that and then changing the cos 2x and sin 2x factors you can show that
cos 3x = cos^ 3x - 3 sin^2 x cos x