Solving Coulombs Law & Trig via Diagram

[prof chaos]

Sorry if I'm doing this wrong... first time poster.

Homework Statement

The diagram gives the relevant info. All three q's are equal point charges of m=0.10 kg. I'm trying to find the value of q.

Homework Equations

Coulombs law and basic trig.

The Attempt at a Solution

Considering either of the outer point charges, I have thus figured out that F_x=Tsinθ and mg=Tcosθ. Dividing those gives F=mgTanθ=0.98N

I can't figure out what to do at all for the second part where I use Coulombs law to combine the the forces of both charges on the most right one. My prof gave the following HW explanation, but I don't understand it:

$$\frac{Kq^2}{(Lsin\Theta)^2}$$ -- $$\frac{kq^2}{(2Lsin\Theta)^2}$$ = $$\frac{5kq^2}{4L^2(sin^2)\Theta}$$

I can rearrange and solve from there... I understand where $$\frac{Kq^2}{(Lsin\Theta)^2}$$ -- $$\frac{kq^2}{(2Lsin\Theta)^2}$$ comes from but how in the world does that turn into $$\frac{5kq^2}{4L^2(sin^2)\Theta}$$

Ugh it turned my thetas into 952;... I hope you still understand it.

 

[rl.bhat]

Hi prof chaos, welcome to PF.

It is simple addition.

1 + 1/4 = 5/4.