Verified answer

csc(θ) * (sin^2(θ) + cos^2(θ)tan(θ))/(sin(θ) + cos(θ)) = csc(θ) * (sin^2(θ) + sin(θ)cos(θ))/(sin(θ) + cos(θ))

= (sin(θ) + cos(θ))/(sin(θ) + cos(θ)) = 1

Let y= tanθ sinθ + cosθ y= (sin^2 θ/cos θ) + cos θ , replacing tan θ = sin θ/cos θ y=(sin^2 θ + cos^2 θ)/cos θ , y= 1/cos θ , utilizing the identity sin^2 θ + cos ^2 θ =1 y= sec θ , for the reason that 1/cos θ = sec θ

You can solve it with arcane tomes of forbidden mathological lore! First you must take the square root of death times life plus 42. then carve the finished equation into an obsidian tablet. Procede to sacrifice 13/4ths of a goat on it. If done correctly it will summon the spirit of arcane math! In order to get your one mathological wish from the spirit, you must answer his one question: Divide Pi by 0. In which you must answer: 42! The spirit of Math is deathly afraid of the number 42 so he will out of fear answer your most arcane math problems. (remember when poaching math spirits gurgle in a hushed tone and recite your times tables backwords. This will keep them from stealing your soul or worse- your division tables!)

PS math spirits don't like the word "Cscθ" (It reminds them of 42) . When you ask them replace "Cscθ" with Steve or Bartholomew

PSS I'm a certified mathomancer and expert in arcane mathology AND successifully divided by 0 on almost 5 occasions (4.9379376 times to be exact)

Using x for theta....

csc(x)(sin^2(x) + cos^2(x)tan(x))/(sin(x) + cos(x))

=csc(x)(sin^2(x) + sin(x)cos(x))/(sin(x) + cos(x))

= (sin^2(x) + sin(x) cos(x))/(sin^2(x) + sin(x)cos(x))

= 1