The diameters of the circumcirle of triangle ABC drawn from A,B and C meet BC, CA and AB, respectively, in L,M and N. Prove that `(1)/(AL) + (1)/(BM) + (1)/(CN) = (2)/(R)`

Explanation

To prove that \(\frac{1}{AL} + \frac{1}{BM} + \frac{1}{CN} = \frac{2}{R}\), where \(R\) is the circumradius of triangle \(ABC\), we will follow these steps:

### Step 1: Understanding the Geometry
We have triangle \(ABC\) with circumcircle \(O\) and diameters \(AL\), \(BM\), and \(CN\) that meet the sides \(BC\), \(CA\), and \(AB\) at points \(L\), \(M\), and \(N\) respectively.

### Step 2: Using the Sine Rule in Triangle OBL
In triangle \(OBL\), we apply the sine rule:
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