Write the equation $\sin^2(x)-3/4$ in alternate form

Question

The equation is: $$\sin^2(x)-(3/4)$$

How do you get this equation in an alternate form, so that there is only division or multiplication present between trigonometric functions.

The solution is: $$\sin(x+π/3)\sin(x-π/3)$$

My try: $$\sin^2(x)-(1/2)-(1/2)*(1/2) = \sin^2(x)-\sin(π/6)-\sin(π/6)*\sin(π/6)$$

Beyond this point I don't know what to do, to get the correct answer
Thank you very much for help

Answer 1

HINT

$$\sin^2 x-\frac34 = \left( \sin x+\frac{\sqrt 3}{2} \right) \left(\sin x-\frac{\sqrt 3}{2} \right)$$

and

$$\sin \frac{\pi}{3}=\frac{\sqrt 3}{2}$$