Unable to find Solution of an Interesting Function !

I was trying really hard on solving this equation in my IIT Coaching class

sin(sin(sin(θ)=cos(θ)

While most of them were busy discussing about their marks and asking others where they went wrong in the exam,I was busy solving this and it was quite bugging actually,no peace only people shouting..How many marks did you get ?Couldn't couldn't concentrate on what i was doing.

There was an awesome and intelligent fellow who didn't care about marks called "Sri Hari",so i spent most of the time with him discussing varies interesting and beautful curves.He brought a book which had amazing mathematical equations such as

x2+y2 = a(x2+y2)1/2

I don't know how these mathematicians plot them without actually substituting values.I can do for a few graphs but not for such complex ones.

So,like i was telling i was really close to finding one more solution of an infinite series,after long calculations i finally landed on the equation which i showed earlier.

So far,I have solved these

y= sin(sin(sin(........∞ (x)))

y=cos(cos(cos(.......∞(x)))

y=tan(tan(tan(.......∞(x)))

The current infinite series which I'm working on is quite huge and challenging,lets see if i manage to solve it.If i did it would be quite a remarkable thing to do.

I wanted to show my papers on the infinte series to my FIITJEE sir but i was scared that he would say that I'm not concetrating on JEE preparation and doing all this shit instead.

I will definitely show him my papers if i come up with the solution on this infinte series !