Assertion $(A)$: If $A=15^{\circ}, B=17^{\circ}$ and $C=13^{\circ}$,then $\cot 2A + \cot 2B + \cot 2C = \cot 2A \cot 2B \cot 2C$.
Reason $(R)$: In a $\triangle PQR$,$\tan \frac{P}{2} \tan \frac{Q}{2} + \tan \frac{Q}{2} \tan \frac{R}{2} + \tan \frac{P}{2} \tan \frac{R}{2} = 1$.
The correct option among the following is:

• A
  $(A)$ is true,$(R)$ is true and $(R)$ is the correct explanation for $(A)$
• B
  $(A)$ is true,$(R)$ is true but $(R)$ is not the correct explanation for $(A)$
• C
  $(A)$ is true but $(R)$ is false
• D
  $(A)$ is false but $(R)$ is true