mathematics - Express the number $2015$ using only the digit $2$ twice

Can you use only two instances of the digit $2$, along with the mathematical operations below, to create an expression that evaluates to $2015$?

Allowed operations:

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  arithmetic operations: addition ($+$), subtraction ($-$), multiplication ($\times$), division ($\div$, or $\frac{x}{y}$), exponentiation (like $2^2$);

  
  


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  factorial ($!$), absolute value ($|...|$);

  
  



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  extraction of the root of any degree in a form $\sqrt[a]{b}$ or the square root in a form $\sqrt{b}$;

  
  


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  trigonometric functions: sine, cosine, tangent, cotangent, secant, cosecant

  
  


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  inverse trigonometric functions: arcsine, arccosine, arctangent, arccotangent, arcsecant, arccosecant

  
  


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  natural logarithm ($\ln b$), or logarithm with any base ($\log_a b$)

  
  

Parentheses $()$ are also allowed.

What is not allowed:

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  digits other than $2$, or more than two instances of the digit $2$

  
  


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  named constants such as $\pi, e$, etc...

  
  


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  defining and using your own functions

  
  


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  other variables

  
  

Example with three $2$s:

A couple of years ago, I managed to solve the same kind of problem, with three $2$s:

We can express any natural number $A$ using three $2$s and the above operations, like this: $$-\log_2\log_2\underbrace{\sqrt{\sqrt{...\sqrt{2}}}}_{A\,\mathrm{square\,roots}}$$

But I couldn't crack the problem using only two $2$s...

Answer

This answer describes a method using trigonometric operations to obtain the square root of any rational number from 0. In this answer, Daniil Agashiyev notes that $\tan\arcsin\cos\arctan\cos\arctan\sqrt{n}=\sqrt{n+1}$.

Using this, we can write 2015 as:

$$(\underbrace{\tan\arcsin\cos\arctan\cos\arctan}_{2011\text{ times}}\,2)^2$$

or even with only one 2:

$$\underbrace{\tan\arcsin\cos\arctan\cos\arctan}_{2015^2-4\text{ times}}\,2$$

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Unlike the linked problem, we're allowed to use the secant and cosecant here, so we can use $\sec\arctan$ or $\newcommand{\arccot}{\operatorname{arccot}}\csc\arccot$ for the same effect.