Please take a look at DEVON's trig equation at 9:14
I must be missing something obvious.
If the second had been 3sin 2x it would be a straight forward question.
The way it stands I was able to "reduce" it to the equation
8sin^4 x - 8sin^2 x + 3sin x + 2 = 0
I tested this equation by subst. random values of angles in the original and this one, and got the same results, so it must be right.
(must have been infected with a case of "oldtimers' disease)
2-2sin^2 x + 3 sinx=0
sin^2 x - 3/2 sin x - 1=0
sinx= (3/2 +-sqrt(9/4 +4) /2
sinx= 3/4 +- 5/4
sin x= -1/2 works.
Of course, of course, I knew it had to be that easy
I read the exponent as a multiplier of x
i.e. 2 cos^2 (2x) + 3 sin x .....