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)

2cos^2x+3sinx=0
2-2sin^2 x + 3 sinx=0
sin^2 x - 3/2 sin x - 1=0

quadratic equation..

sinx= (3/2 +-sqrt(9/4 +4) /2
sinx= 3/4 +- 5/4

sin x= -1/2 works.

check me.

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 .....